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Sample records for nonlinear programming problem

  1. Bonus algorithm for large scale stochastic nonlinear programming problems

    CERN Document Server

    Diwekar, Urmila

    2015-01-01

    This book presents the details of the BONUS algorithm and its real world applications in areas like sensor placement in large scale drinking water networks, sensor placement in advanced power systems, water management in power systems, and capacity expansion of energy systems. A generalized method for stochastic nonlinear programming based on a sampling based approach for uncertainty analysis and statistical reweighting to obtain probability information is demonstrated in this book. Stochastic optimization problems are difficult to solve since they involve dealing with optimization and uncertainty loops. There are two fundamental approaches used to solve such problems. The first being the decomposition techniques and the second method identifies problem specific structures and transforms the problem into a deterministic nonlinear programming problem. These techniques have significant limitations on either the objective function type or the underlying distributions for the uncertain variables. Moreover, these ...

  2. COYOTE: a finite element computer program for nonlinear heat conduction problems

    International Nuclear Information System (INIS)

    Gartling, D.K.

    1978-06-01

    COYOTE is a finite element computer program designed for the solution of two-dimensional, nonlinear heat conduction problems. The theoretical and mathematical basis used to develop the code is described. Program capabilities and complete user instructions are presented. Several example problems are described in detail to demonstrate the use of the program

  3. A quadratic approximation-based algorithm for the solution of multiparametric mixed-integer nonlinear programming problems

    KAUST Repository

    Domí nguez, Luis F.; Pistikopoulos, Efstratios N.

    2012-01-01

    An algorithm for the solution of convex multiparametric mixed-integer nonlinear programming problems arising in process engineering problems under uncertainty is introduced. The proposed algorithm iterates between a multiparametric nonlinear

  4. A Smooth Newton Method for Nonlinear Programming Problems with Inequality Constraints

    Directory of Open Access Journals (Sweden)

    Vasile Moraru

    2012-02-01

    Full Text Available The paper presents a reformulation of the Karush-Kuhn-Tucker (KKT system associated nonlinear programming problem into an equivalent system of smooth equations. Classical Newton method is applied to solve the system of equations. The superlinear convergence of the primal sequence, generated by proposed method, is proved. The preliminary numerical results with a problems test set are presented.

  5. TRUMP3-JR: a finite difference computer program for nonlinear heat conduction problems

    International Nuclear Information System (INIS)

    Ikushima, Takeshi

    1984-02-01

    Computer program TRUMP3-JR is a revised version of TRUMP3 which is a finite difference computer program used for the solution of multi-dimensional nonlinear heat conduction problems. Pre- and post-processings for input data generation and graphical representations of calculation results of TRUMP3 are avaiable in TRUMP3-JR. The calculation equations, program descriptions and user's instruction are presented. A sample problem is described to demonstrate the use of the program. (author)

  6. A quadratic approximation-based algorithm for the solution of multiparametric mixed-integer nonlinear programming problems

    KAUST Repository

    Domínguez, Luis F.

    2012-06-25

    An algorithm for the solution of convex multiparametric mixed-integer nonlinear programming problems arising in process engineering problems under uncertainty is introduced. The proposed algorithm iterates between a multiparametric nonlinear programming subproblem and a mixed-integer nonlinear programming subproblem to provide a series of parametric upper and lower bounds. The primal subproblem is formulated by fixing the integer variables and solved through a series of multiparametric quadratic programming (mp-QP) problems based on quadratic approximations of the objective function, while the deterministic master subproblem is formulated so as to provide feasible integer solutions for the next primal subproblem. To reduce the computational effort when infeasibilities are encountered at the vertices of the critical regions (CRs) generated by the primal subproblem, a simplicial approximation approach is used to obtain CRs that are feasible at each of their vertices. The algorithm terminates when there does not exist an integer solution that is better than the one previously used by the primal problem. Through a series of examples, the proposed algorithm is compared with a multiparametric mixed-integer outer approximation (mp-MIOA) algorithm to demonstrate its computational advantages. © 2012 American Institute of Chemical Engineers (AIChE).

  7. A Kind of Nonlinear Programming Problem Based on Mixed Fuzzy Relation Equations Constraints

    Science.gov (United States)

    Li, Jinquan; Feng, Shuang; Mi, Honghai

    In this work, a kind of nonlinear programming problem with non-differential objective function and under the constraints expressed by a system of mixed fuzzy relation equations is investigated. First, some properties of this kind of optimization problem are obtained. Then, a polynomial-time algorithm for this kind of optimization problem is proposed based on these properties. Furthermore, we show that this algorithm is optimal for the considered optimization problem in this paper. Finally, numerical examples are provided to illustrate our algorithms.

  8. CASKETSS-HEAT: a finite difference computer program for nonlinear heat conduction problems

    International Nuclear Information System (INIS)

    Ikushima, Takeshi

    1988-12-01

    A heat conduction program CASKETSS-HEAT has been developed. CASKETSS-HEAT is a finite difference computer program used for the solution of multi-dimensional nonlinear heat conduction problems. Main features of CASKETSS-HEAT are as follows. (1) One, two and three-dimensional geometries for heat conduction calculation are available. (2) Convection and radiation heat transfer of boundry can be specified. (3) Phase change and chemical change can be treated. (4) Finned surface heat transfer can be treated easily. (5) Data memory allocation in the program is variable according to problem size. (6) The program is a compatible heat transfer analysis program to the stress analysis program SAP4 and SAP5. (7) Pre- and post-processing for input data generation and graphic representation of calculation results are available. In the paper, brief illustration of calculation method, input data and sample calculation are presented. (author)

  9. Recent advances in multiparametric nonlinear programming

    KAUST Repository

    Domí nguez, Luis F.; Narciso, Diogo A.; Pistikopoulos, Efstratios N.

    2010-01-01

    In this paper, we present recent developments in multiparametric nonlinear programming. For the case of convex problems, we highlight key issues regarding the full characterization of the parametric solution space and we discuss, through an illustrative example problem, four alternative state-of-the-art multiparametric nonlinear programming algorithms. We also identify a number of main challenges for the non-convex case and highlight future research directions. © 2009 Elsevier Ltd. All rights reserved.

  10. Recent advances in multiparametric nonlinear programming

    KAUST Repository

    Domínguez, Luis F.

    2010-05-01

    In this paper, we present recent developments in multiparametric nonlinear programming. For the case of convex problems, we highlight key issues regarding the full characterization of the parametric solution space and we discuss, through an illustrative example problem, four alternative state-of-the-art multiparametric nonlinear programming algorithms. We also identify a number of main challenges for the non-convex case and highlight future research directions. © 2009 Elsevier Ltd. All rights reserved.

  11. Intuitionistic Fuzzy Goal Programming Technique for Solving Non-Linear Multi-objective Structural Problem

    Directory of Open Access Journals (Sweden)

    Samir Dey

    2015-07-01

    Full Text Available This paper proposes a new multi-objective intuitionistic fuzzy goal programming approach to solve a multi-objective nonlinear programming problem in context of a structural design. Here we describe some basic properties of intuitionistic fuzzy optimization. We have considered a multi-objective structural optimization problem with several mutually conflicting objectives. The design objective is to minimize weight of the structure and minimize the vertical deflection at loading point of a statistically loaded three-bar planar truss subjected to stress constraints on each of the truss members. This approach is used to solve the above structural optimization model based on arithmetic mean and compare with the solution by intuitionistic fuzzy goal programming approach. A numerical solution is given to illustrate our approach.

  12. Indefinitely preconditioned inexact Newton method for large sparse equality constrained non-linear programming problems

    Czech Academy of Sciences Publication Activity Database

    Lukšan, Ladislav; Vlček, Jan

    1998-01-01

    Roč. 5, č. 3 (1998), s. 219-247 ISSN 1070-5325 R&D Projects: GA ČR GA201/96/0918 Keywords : nonlinear programming * sparse problems * equality constraints * truncated Newton method * augmented Lagrangian function * indefinite systems * indefinite preconditioners * conjugate gradient method * residual smoothing Subject RIV: BA - General Mathematics Impact factor: 0.741, year: 1998

  13. JAC, 2-D Finite Element Method Program for Quasi Static Mechanics Problems by Nonlinear Conjugate Gradient (CG) Method

    International Nuclear Information System (INIS)

    Biffle, J.H.

    1991-01-01

    1 - Description of program or function: JAC is a two-dimensional finite element program for solving large deformation, temperature dependent, quasi-static mechanics problems with the nonlinear conjugate gradient (CG) technique. Either plane strain or axisymmetric geometry may be used with material descriptions which include temperature dependent elastic-plastic, temperature dependent secondary creep, and isothermal soil models. The nonlinear effects examined include material and geometric nonlinearities due to large rotations, large strains, and surface which slide relative to one another. JAC is vectorized to perform efficiently on the Cray1 computer. A restart capability is included. 2 - Method of solution: The nonlinear conjugate gradient method is employed in a two-dimensional plane strain or axisymmetric setting with various techniques for accelerating convergence. Sliding interface conditions are also implemented. A four-node Lagrangian uniform strain element is used with orthogonal hourglass viscosity to control the zero energy modes. Three sets of continuum equations are needed - kinematic statements, constitutive equations, and equations of equilibrium - to describe the deformed configuration of the body. 3 - Restrictions on the complexity of the problem - Maxima of: 10 load and solution control functions, 4 materials. The strain rate is assumed constant over a time interval. Current large rotation theory is applicable to a maximum shear strain of 1.0. JAC should be used with caution for large shear strains. Problem size is limited only by available memory

  14. θ-convex nonlinear programming problems

    International Nuclear Information System (INIS)

    Emam, T.

    2008-01-01

    A class of sets and a class of functions called θ-convex sets and θ-convex functions are introduced by relaxing the definitions of convex sets and operator θ on the sets and domain of definition of the functions. The optimally results for θ-convex programming problems are established.

  15. ROTAX: a nonlinear optimization program by axes rotation method

    International Nuclear Information System (INIS)

    Suzuki, Tadakazu

    1977-09-01

    A nonlinear optimization program employing the axes rotation method has been developed for solving nonlinear problems subject to nonlinear inequality constraints and its stability and convergence efficiency were examined. The axes rotation method is a direct search of the optimum point by rotating the orthogonal coordinate system in a direction giving the minimum objective. The searching direction is rotated freely in multi-dimensional space, so the method is effective for the problems represented with the contours having deep curved valleys. In application of the axes rotation method to the optimization problems subject to nonlinear inequality constraints, an improved version of R.R. Allran and S.E.J. Johnsen's method is used, which deals with a new objective function composed of the original objective and a penalty term to consider the inequality constraints. The program is incorporated in optimization code system SCOOP. (auth.)

  16. Applications and algorithms for mixed integer nonlinear programming

    International Nuclear Information System (INIS)

    Leyffer, Sven; Munson, Todd; Linderoth, Jeff; Luedtke, James; Miller, Andrew

    2009-01-01

    The mathematical modeling of systems often requires the use of both nonlinear and discrete components. Discrete decision variables model dichotomies, discontinuities, and general logical relationships. Nonlinear functions are required to accurately represent physical properties such as pressure, stress, temperature, and equilibrium. Problems involving both discrete variables and nonlinear constraint functions are known as mixed-integer nonlinear programs (MINLPs) and are among the most challenging computational optimization problems faced by researchers and practitioners. In this paper, we describe relevant scientific applications that are naturally modeled as MINLPs, we provide an overview of available algorithms and software, and we describe ongoing methodological advances for solving MINLPs. These algorithmic advances are making increasingly larger instances of this important family of problems tractable.

  17. Problems in nonlinear resistive MHD

    International Nuclear Information System (INIS)

    Turnbull, A.D.; Strait, E.J.; La Haye, R.J.; Chu, M.S.; Miller, R.L.

    1998-01-01

    Two experimentally relevant problems can relatively easily be tackled by nonlinear MHD codes. Both problems require plasma rotation in addition to the nonlinear mode coupling and full geometry already incorporated into the codes, but no additional physics seems to be crucial. These problems discussed here are: (1) nonlinear coupling and interaction of multiple MHD modes near the B limit and (2) nonlinear coupling of the m/n = 1/1 sawtooth mode with higher n gongs and development of seed islands outside q = 1

  18. Nonlinear programming for classification problems in machine learning

    Science.gov (United States)

    Astorino, Annabella; Fuduli, Antonio; Gaudioso, Manlio

    2016-10-01

    We survey some nonlinear models for classification problems arising in machine learning. In the last years this field has become more and more relevant due to a lot of practical applications, such as text and web classification, object recognition in machine vision, gene expression profile analysis, DNA and protein analysis, medical diagnosis, customer profiling etc. Classification deals with separation of sets by means of appropriate separation surfaces, which is generally obtained by solving a numerical optimization model. While linear separability is the basis of the most popular approach to classification, the Support Vector Machine (SVM), in the recent years using nonlinear separating surfaces has received some attention. The objective of this work is to recall some of such proposals, mainly in terms of the numerical optimization models. In particular we tackle the polyhedral, ellipsoidal, spherical and conical separation approaches and, for some of them, we also consider the semisupervised versions.

  19. A chaos-based evolutionary algorithm for general nonlinear programming problems

    International Nuclear Information System (INIS)

    El-Shorbagy, M.A.; Mousa, A.A.; Nasr, S.M.

    2016-01-01

    In this paper we present a chaos-based evolutionary algorithm (EA) for solving nonlinear programming problems named chaotic genetic algorithm (CGA). CGA integrates genetic algorithm (GA) and chaotic local search (CLS) strategy to accelerate the optimum seeking operation and to speed the convergence to the global solution. The integration of global search represented in genetic algorithm and CLS procedures should offer the advantages of both optimization methods while offsetting their disadvantages. By this way, it is intended to enhance the global convergence and to prevent to stick on a local solution. The inherent characteristics of chaos can enhance optimization algorithms by enabling it to escape from local solutions and increase the convergence to reach to the global solution. Twelve chaotic maps have been analyzed in the proposed approach. The simulation results using the set of CEC’2005 show that the application of chaotic mapping may be an effective strategy to improve the performances of EAs.

  20. Nonlinear programming with feedforward neural networks.

    Energy Technology Data Exchange (ETDEWEB)

    Reifman, J.

    1999-06-02

    We provide a practical and effective method for solving constrained optimization problems by successively training a multilayer feedforward neural network in a coupled neural-network/objective-function representation. Nonlinear programming problems are easily mapped into this representation which has a simpler and more transparent method of solution than optimization performed with Hopfield-like networks and poses very mild requirements on the functions appearing in the problem. Simulation results are illustrated and compared with an off-the-shelf optimization tool.

  1. WHAMSE: a program for three-dimensional nonlinear structural dynamics

    International Nuclear Information System (INIS)

    Belytschko, T.; Tsay, C.S.

    1982-02-01

    WHAMSE is a computer program for the nonlinear, transient analysis of structures. The formulation includes both geometric and material nonlinearities, so problems with large displacements and elastic-plastic behavior can be treated. Explicit time integration is used, so the program is most suitable for implusive loads. Energy balance calculations are provided to check numerical stability. The mass matrix is lumped. A finite element format is used for the description of the problem geometry, so the program is quite versatile in treating complex engineering structures. The following elements are included: a triangular element for thin plates and shells, a beam element, a spring element and a rigid body. Mesh generation features are provided to simplify program input. Other features of the program are: (1) a restart capability; (2) a variety of output options, such as printer plots or CALCOMP plots of selected time histories, picture (snapshot) output, and CALCOMP plots of the undeformed and deformed structure

  2. PLANS; a finite element program for nonlinear analysis of structures. Volume 2: User's manual

    Science.gov (United States)

    Pifko, A.; Armen, H., Jr.; Levy, A.; Levine, H.

    1977-01-01

    The PLANS system, rather than being one comprehensive computer program, is a collection of finite element programs used for the nonlinear analysis of structures. This collection of programs evolved and is based on the organizational philosophy in which classes of analyses are treated individually based on the physical problem class to be analyzed. Each of the independent finite element computer programs of PLANS, with an associated element library, can be individually loaded and used to solve the problem class of interest. A number of programs have been developed for material nonlinear behavior alone and for combined geometric and material nonlinear behavior. The usage, capabilities, and element libraries of the current programs include: (1) plastic analysis of built-up structures where bending and membrane effects are significant, (2) three dimensional elastic-plastic analysis, (3) plastic analysis of bodies of revolution, and (4) material and geometric nonlinear analysis of built-up structures.

  3. Robust Optimization Using Supremum of the Objective Function for Nonlinear Programming Problems

    International Nuclear Information System (INIS)

    Lee, Se Jung; Park, Gyung Jin

    2014-01-01

    In the robust optimization field, the robustness of the objective function emphasizes an insensitive design. In general, the robustness of the objective function can be achieved by reducing the change of the objective function with respect to the variation of the design variables and parameters. However, in conventional methods, when an insensitive design is emphasized, the performance of the objective function can be deteriorated. Besides, if the numbers of the design variables are increased, the numerical cost is quite high in robust optimization for nonlinear programming problems. In this research, the robustness index for the objective function and a process of robust optimization are proposed. Moreover, a method using the supremum of linearized functions is also proposed to reduce the computational cost. Mathematical examples are solved for the verification of the proposed method and the results are compared with those from the conventional methods. The proposed approach improves the performance of the objective function and its efficiency

  4. Nonlinear Elliptic Boundary Value Problems at Resonance with Nonlinear Wentzell Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Ciprian G. Gal

    2017-01-01

    Full Text Available Given a bounded domain Ω⊂RN with a Lipschitz boundary ∂Ω and p,q∈(1,+∞, we consider the quasilinear elliptic equation -Δpu+α1u=f in Ω complemented with the generalized Wentzell-Robin type boundary conditions of the form bx∇up-2∂nu-ρbxΔq,Γu+α2u=g on ∂Ω. In the first part of the article, we give necessary and sufficient conditions in terms of the given functions f, g and the nonlinearities α1, α2, for the solvability of the above nonlinear elliptic boundary value problems with the nonlinear boundary conditions. In other words, we establish a sort of “nonlinear Fredholm alternative” for our problem which extends the corresponding Landesman and Lazer result for elliptic problems with linear homogeneous boundary conditions. In the second part, we give some additional results on existence and uniqueness and we study the regularity of the weak solutions for these classes of nonlinear problems. More precisely, we show some global a priori estimates for these weak solutions in an L∞-setting.

  5. A nonlinear oscillatory problem

    International Nuclear Information System (INIS)

    Zhou Qingqing.

    1991-10-01

    We have studied the nonlinear oscillatory problem of orthotropic cylindrical shell, we have analyzed the character of the oscillatory system. The stable condition of the oscillatory system has been given. (author). 6 refs

  6. Contribution of Fuzzy Minimal Cost Flow Problem by Possibility Programming

    OpenAIRE

    S. Fanati Rashidi; A. A. Noora

    2010-01-01

    Using the concept of possibility proposed by zadeh, luhandjula ([4,8]) and buckley ([1]) have proposed the possibility programming. The formulation of buckley results in nonlinear programming problems. Negi [6]re-formulated the approach of Buckley by the use of trapezoidal fuzzy numbers and reduced the problem into fuzzy linear programming problem. Shih and Lee ([7]) used the Negi approach to solve a minimum cost flow problem, whit fuzzy costs and the upper and lower bound. ...

  7. Overlapping Schwarz for Nonlinear Problems. An Element Agglomeration Nonlinear Additive Schwarz Preconditioned Newton Method for Unstructured Finite Element Problems

    Energy Technology Data Exchange (ETDEWEB)

    Cai, X C; Marcinkowski, L; Vassilevski, P S

    2005-02-10

    This paper extends previous results on nonlinear Schwarz preconditioning ([4]) to unstructured finite element elliptic problems exploiting now nonlocal (but small) subspaces. The non-local finite element subspaces are associated with subdomains obtained from a non-overlapping element partitioning of the original set of elements and are coarse outside the prescribed element subdomain. The coarsening is based on a modification of the agglomeration based AMGe method proposed in [8]. Then, the algebraic construction from [9] of the corresponding non-linear finite element subproblems is applied to generate the subspace based nonlinear preconditioner. The overall nonlinearly preconditioned problem is solved by an inexact Newton method. Numerical illustration is also provided.

  8. A nonlinear bi-level programming approach for product portfolio management.

    Science.gov (United States)

    Ma, Shuang

    2016-01-01

    Product portfolio management (PPM) is a critical decision-making for companies across various industries in today's competitive environment. Traditional studies on PPM problem have been motivated toward engineering feasibilities and marketing which relatively pay less attention to other competitors' actions and the competitive relations, especially in mathematical optimization domain. The key challenge lies in that how to construct a mathematical optimization model to describe this Stackelberg game-based leader-follower PPM problem and the competitive relations between them. The primary work of this paper is the representation of a decision framework and the optimization model to leverage the PPM problem of leader and follower. A nonlinear, integer bi-level programming model is developed based on the decision framework. Furthermore, a bi-level nested genetic algorithm is put forward to solve this nonlinear bi-level programming model for leader-follower PPM problem. A case study of notebook computer product portfolio optimization is reported. Results and analyses reveal that the leader-follower bi-level optimization model is robust and can empower product portfolio optimization.

  9. Multisplitting for linear, least squares and nonlinear problems

    Energy Technology Data Exchange (ETDEWEB)

    Renaut, R.

    1996-12-31

    In earlier work, presented at the 1994 Iterative Methods meeting, a multisplitting (MS) method of block relaxation type was utilized for the solution of the least squares problem, and nonlinear unconstrained problems. This talk will focus on recent developments of the general approach and represents joint work both with Andreas Frommer, University of Wupertal for the linear problems and with Hans Mittelmann, Arizona State University for the nonlinear problems.

  10. Multigrid Reduction in Time for Nonlinear Parabolic Problems

    Energy Technology Data Exchange (ETDEWEB)

    Falgout, R. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Manteuffel, T. A. [Univ. of Colorado, Boulder, CO (United States); O' Neill, B. [Univ. of Colorado, Boulder, CO (United States); Schroder, J. B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2016-01-04

    The need for parallel-in-time is being driven by changes in computer architectures, where future speed-ups will be available through greater concurrency, but not faster clock speeds, which are stagnant.This leads to a bottleneck for sequential time marching schemes, because they lack parallelism in the time dimension. Multigrid Reduction in Time (MGRIT) is an iterative procedure that allows for temporal parallelism by utilizing multigrid reduction techniques and a multilevel hierarchy of coarse time grids. MGRIT has been shown to be effective for linear problems, with speedups of up to 50 times. The goal of this work is the efficient solution of nonlinear problems with MGRIT, where efficient is defined as achieving similar performance when compared to a corresponding linear problem. As our benchmark, we use the p-Laplacian, where p = 4 corresponds to a well-known nonlinear diffusion equation and p = 2 corresponds to our benchmark linear diffusion problem. When considering linear problems and implicit methods, the use of optimal spatial solvers such as spatial multigrid imply that the cost of one time step evaluation is fixed across temporal levels, which have a large variation in time step sizes. This is not the case for nonlinear problems, where the work required increases dramatically on coarser time grids, where relatively large time steps lead to worse conditioned nonlinear solves and increased nonlinear iteration counts per time step evaluation. This is the key difficulty explored by this paper. We show that by using a variety of strategies, most importantly, spatial coarsening and an alternate initial guess to the nonlinear time-step solver, we can reduce the work per time step evaluation over all temporal levels to a range similar with the corresponding linear problem. This allows for parallel scaling behavior comparable to the corresponding linear problem.

  11. Nonlinear acceleration of transport criticality problems

    International Nuclear Information System (INIS)

    Park, H.; Knoll, D.A.; Newman, C.K.

    2011-01-01

    We present a nonlinear acceleration algorithm for the transport criticality problem. The algorithm combines the well-known nonlinear diffusion acceleration (NDA) with a recently developed, Newton-based, nonlinear criticality acceleration (NCA) algorithm. The algorithm first employs the NDA to reduce the system to scalar flux, then the NCA is applied to the resulting drift-diffusion system. We apply a nonlinear elimination technique to eliminate the eigenvalue from the Jacobian matrix. Numerical results show that the algorithm reduces the CPU time a factor of 400 in a very diffusive system, and a factor of 5 in a non-diffusive system. (author)

  12. Implementation of the - Constraint Method in Special Class of Multi-objective Fuzzy Bi-Level Nonlinear Problems

    Directory of Open Access Journals (Sweden)

    Azza Hassan Amer

    2017-12-01

    Full Text Available Geometric programming problem is a powerful tool for solving some special type nonlinear programming problems. In the last few years we have seen a very rapid development on solving multiobjective geometric programming problem. A few mathematical programming methods namely fuzzy programming, goal programming and weighting methods have been applied in the recent past to find the compromise solution. In this paper, -constraint method has been applied in bi-level multiobjective geometric programming problem to find the Pareto optimal solution at each level. The equivalent mathematical programming problems are formulated to find their corresponding value of the objective function based on the duality theorem at eash level. Here, we have developed a new algorithm for fuzzy programming technique to solve bi-level multiobjective geometric programming problems to find an optimal compromise solution. Finally the solution procedure of the fuzzy technique is illustrated by a numerical example

  13. Multiparametric programming based algorithms for pure integer and mixed-integer bilevel programming problems

    KAUST Repository

    Domínguez, Luis F.

    2010-12-01

    This work introduces two algorithms for the solution of pure integer and mixed-integer bilevel programming problems by multiparametric programming techniques. The first algorithm addresses the integer case of the bilevel programming problem where integer variables of the outer optimization problem appear in linear or polynomial form in the inner problem. The algorithm employs global optimization techniques to convexify nonlinear terms generated by a reformulation linearization technique (RLT). A continuous multiparametric programming algorithm is then used to solve the reformulated convex inner problem. The second algorithm addresses the mixed-integer case of the bilevel programming problem where integer and continuous variables of the outer problem appear in linear or polynomial forms in the inner problem. The algorithm relies on the use of global multiparametric mixed-integer programming techniques at the inner optimization level. In both algorithms, the multiparametric solutions obtained are embedded in the outer problem to form a set of single-level (M)(I)(N)LP problems - which are then solved to global optimality using standard fixed-point (global) optimization methods. Numerical examples drawn from the open literature are presented to illustrate the proposed algorithms. © 2010 Elsevier Ltd.

  14. Determination of Nonlinear Stiffness Coefficients for Finite Element Models with Application to the Random Vibration Problem

    Science.gov (United States)

    Muravyov, Alexander A.

    1999-01-01

    In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.

  15. Contribution of Fuzzy Minimal Cost Flow Problem by Possibility Programming

    Directory of Open Access Journals (Sweden)

    S. Fanati Rashidi

    2010-06-01

    Full Text Available Using the concept of possibility proposed by zadeh, luhandjula ([4,8] and buckley ([1] have proposed the possibility programming. The formulation of buckley results in nonlinear programming problems. Negi [6]re-formulated the approach of Buckley by the use of trapezoidal fuzzy numbers and reduced the problem into fuzzy linear programming problem. Shih and Lee ([7] used the Negi approach to solve a minimum cost flow problem, whit fuzzy costs and the upper and lower bound. In this paper we shall consider the general form of this problem where all of the parameters and variables are fuzzy and also a model for solving is proposed

  16. Combined algorithms in nonlinear problems of magnetostatics

    International Nuclear Information System (INIS)

    Gregus, M.; Khoromskij, B.N.; Mazurkevich, G.E.; Zhidkov, E.P.

    1988-01-01

    To solve boundary problems of magnetostatics in unbounded two- and three-dimensional regions, we construct combined algorithms based on a combination of the method of boundary integral equations with the grid methods. We study the question of substantiation of the combined method of nonlinear magnetostatic problem without the preliminary discretization of equations and give some results on the convergence of iterative processes that arise in non-linear cases. We also discuss economical iterative processes and algorithms that solve boundary integral equations on certain surfaces. Finally, examples of numerical solutions of magnetostatic problems that arose when modelling the fields of electrophysical installations are given too. 14 refs.; 2 figs.; 1 tab

  17. ARSTEC, Nonlinear Optimization Program Using Random Search Method

    International Nuclear Information System (INIS)

    Rasmuson, D. M.; Marshall, N. H.

    1979-01-01

    1 - Description of problem or function: The ARSTEC program was written to solve nonlinear, mixed integer, optimization problems. An example of such a problem in the nuclear industry is the allocation of redundant parts in the design of a nuclear power plant to minimize plant unavailability. 2 - Method of solution: The technique used in ARSTEC is the adaptive random search method. The search is started from an arbitrary point in the search region and every time a point that improves the objective function is found, the search region is centered at that new point. 3 - Restrictions on the complexity of the problem: Presently, the maximum number of independent variables allowed is 10. This can be changed by increasing the dimension of the arrays

  18. Higher-order techniques for some problems of nonlinear control

    Directory of Open Access Journals (Sweden)

    Sarychev Andrey V.

    2002-01-01

    Full Text Available A natural first step when dealing with a nonlinear problem is an application of some version of linearization principle. This includes the well known linearization principles for controllability, observability and stability and also first-order optimality conditions such as Lagrange multipliers rule or Pontryagin's maximum principle. In many interesting and important problems of nonlinear control the linearization principle fails to provide a solution. In the present paper we provide some examples of how higher-order methods of differential geometric control theory can be used for the study nonlinear control systems in such cases. The presentation includes: nonlinear systems with impulsive and distribution-like inputs; second-order optimality conditions for bang–bang extremals of optimal control problems; methods of high-order averaging for studying stability and stabilization of time-variant control systems.

  19. Advanced Research Workshop on Nonlinear Hyperbolic Problems

    CERN Document Server

    Serre, Denis; Raviart, Pierre-Arnaud

    1987-01-01

    The field of nonlinear hyperbolic problems has been expanding very fast over the past few years, and has applications - actual and potential - in aerodynamics, multifluid flows, combustion, detonics amongst other. The difficulties that arise in application are of theoretical as well as numerical nature. In fact, the papers in this volume of proceedings deal to a greater extent with theoretical problems emerging in the resolution of nonlinear hyperbolic systems than with numerical methods. The volume provides an excellent up-to-date review of the current research trends in this area.

  20. Nonlinear Knowledge in Kernel-Based Multiple Criteria Programming Classifier

    Science.gov (United States)

    Zhang, Dongling; Tian, Yingjie; Shi, Yong

    Kernel-based Multiple Criteria Linear Programming (KMCLP) model is used as classification methods, which can learn from training examples. Whereas, in traditional machine learning area, data sets are classified only by prior knowledge. Some works combine the above two classification principle to overcome the defaults of each approach. In this paper, we propose a model to incorporate the nonlinear knowledge into KMCLP in order to solve the problem when input consists of not only training example, but also nonlinear prior knowledge. In dealing with real world case breast cancer diagnosis, the model shows its better performance than the model solely based on training data.

  1. Nonlinear singular perturbation problems of arbitrary real orders

    International Nuclear Information System (INIS)

    Bijura, Angelina M.

    2003-10-01

    Higher order asymptotic solutions of singularly perturbed nonlinear fractional integral and derivatives of order 1/2 are investigated. It is particularly shown that whilst certain asymptotic expansions are applied successfully to linear equations and particular nonlinear problems, the standard formal asymptotic expansion is appropriate for the general class of nonlinear equations. This theory is then generalised to the general equation (of order β, 0 < β < 1). (author)

  2. Solving Large Scale Nonlinear Eigenvalue Problem in Next-Generation Accelerator Design

    Energy Technology Data Exchange (ETDEWEB)

    Liao, Ben-Shan; Bai, Zhaojun; /UC, Davis; Lee, Lie-Quan; Ko, Kwok; /SLAC

    2006-09-28

    A number of numerical methods, including inverse iteration, method of successive linear problem and nonlinear Arnoldi algorithm, are studied in this paper to solve a large scale nonlinear eigenvalue problem arising from finite element analysis of resonant frequencies and external Q{sub e} values of a waveguide loaded cavity in the next-generation accelerator design. They present a nonlinear Rayleigh-Ritz iterative projection algorithm, NRRIT in short and demonstrate that it is the most promising approach for a model scale cavity design. The NRRIT algorithm is an extension of the nonlinear Arnoldi algorithm due to Voss. Computational challenges of solving such a nonlinear eigenvalue problem for a full scale cavity design are outlined.

  3. Electric generating capacity planning: A nonlinear programming approach

    Energy Technology Data Exchange (ETDEWEB)

    Yakin, M.Z.; McFarland, J.W.

    1987-02-01

    This paper presents a nonlinear programming approach for long-range generating capacity expansion planning in electrical power systems. The objective in the model is the minimization of total cost consisting of investment cost plus generation cost for a multi-year planning horizon. Reliability constraints are imposed by using standard and practical reserve margin requirements. State equations representing the dynamic aspect of the problem are included. The electricity demand (load) and plant availabilities are treated as random variables, and the method of cumulants is used to calculate the expected energy generated by each plant in each year of the planning horizon. The resulting model has a (highly) nonlinear objective function and linear constraints. The planning model is solved over the multiyear planning horizon instead of decomposing it into one-year period problems. This approach helps the utility decision maker to carry out extensive sensitivity analysis easily. A case study example is provided using EPRI test data. Relationships among the reserve margin, total cost and surplus energy generating capacity over the planning horizon are explored by analyzing the model.

  4. Nonlinear programming analysis and methods

    CERN Document Server

    Avriel, Mordecai

    2012-01-01

    This text provides an excellent bridge between principal theories and concepts and their practical implementation. Topics include convex programming, duality, generalized convexity, analysis of selected nonlinear programs, techniques for numerical solutions, and unconstrained optimization methods.

  5. A Recurrent Neural Network for Nonlinear Fractional Programming

    Directory of Open Access Journals (Sweden)

    Quan-Ju Zhang

    2012-01-01

    Full Text Available This paper presents a novel recurrent time continuous neural network model which performs nonlinear fractional optimization subject to interval constraints on each of the optimization variables. The network is proved to be complete in the sense that the set of optima of the objective function to be minimized with interval constraints coincides with the set of equilibria of the neural network. It is also shown that the network is primal and globally convergent in the sense that its trajectory cannot escape from the feasible region and will converge to an exact optimal solution for any initial point being chosen in the feasible interval region. Simulation results are given to demonstrate further the global convergence and good performance of the proposing neural network for nonlinear fractional programming problems with interval constraints.

  6. Analytical Solutions to Non-linear Mechanical Oscillation Problems

    DEFF Research Database (Denmark)

    Kaliji, H. D.; Ghadimi, M.; Barari, Amin

    2011-01-01

    In this paper, the Max-Min Method is utilized for solving the nonlinear oscillation problems. The proposed approach is applied to three systems with complex nonlinear terms in their motion equations. By means of this method, the dynamic behavior of oscillation systems can be easily approximated u...

  7. Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach

    Energy Technology Data Exchange (ETDEWEB)

    Pham, Huyên, E-mail: pham@math.univ-paris-diderot.fr; Wei, Xiaoli, E-mail: tyswxl@gmail.com [Laboratoire de Probabilités et Modèles Aléatoires, CNRS, UMR 7599, Université Paris Diderot (France)

    2016-12-15

    We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.

  8. Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach

    International Nuclear Information System (INIS)

    Pham, Huyên; Wei, Xiaoli

    2016-01-01

    We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.

  9. Solving nonlinear nonstationary problem of heat-conductivity by finite element method

    Directory of Open Access Journals (Sweden)

    Антон Янович Карвацький

    2016-11-01

    Full Text Available Methodology and effective solving algorithm of non-linear dynamic problems of thermal and electric conductivity with significant temperature dependence of thermal and physical properties are given on the basis of finite element method (FEM and Newton linearization method. Discrete equations system FEM was obtained with the use of Galerkin method, where the main function is the finite element form function. The methodology based on successive solving problems of thermal and electrical conductivity has been examined in the work in order to minimize the requirements for calculating resources (RAM. in particular. Having used Mathcad software original programming code was developed to solve the given problem. After investigation of the received results, comparative analyses of accurate solution data and results of numerical solutions, obtained with the use of Matlab programming products, was held. The geometry of one fourth part of the finite sized cylinder was used to test the given numerical model. The discretization of the calculation part was fulfilled using the open programming software for automated Gmsh nets with tetrahedral units, while ParaView, which is an open programming code as well, was used to visualize the calculation results. It was found out that the maximum value violation of potential and temperature determination doesn`t exceed 0,2-0,83% in the given work according to the problem conditions

  10. Uncertainty Modeling and Robust Output Feedback Control of Nonlinear Discrete Systems: A Mathematical Programming Approach

    Directory of Open Access Journals (Sweden)

    Olav Slupphaug

    2001-01-01

    Full Text Available We present a mathematical programming approach to robust control of nonlinear systems with uncertain, possibly time-varying, parameters. The uncertain system is given by different local affine parameter dependent models in different parts of the state space. It is shown how this representation can be obtained from a nonlinear uncertain system by solving a set of continuous linear semi-infinite programming problems, and how each of these problems can be solved as a (finite series of ordinary linear programs. Additionally, the system representation includes control- and state constraints. The controller design method is derived from Lyapunov stability arguments and utilizes an affine parameter dependent quadratic Lyapunov function. The controller has a piecewise affine output feedback structure, and the design amounts to finding a feasible solution to a set of linear matrix inequalities combined with one spectral radius constraint on the product of two positive definite matrices. A local solution approach to this nonconvex feasibility problem is proposed. Complexity of the design method and some special cases such as state- feedback are discussed. Finally, an application of the results is given by proposing an on-line computationally feasible algorithm for constrained nonlinear state- feedback model predictive control with robust stability.

  11. A solution to nonlinearity problems

    International Nuclear Information System (INIS)

    Neuffer, D.V.

    1989-01-01

    New methods of correcting dynamic nonlinearities resulting from the multipole content of a synchrotron or transport line are presented. In a simplest form, correction elements are places at the center (C) of the accelerator half-cells as well as near the focusing (F) and defocusing (D) quadrupoles. In a first approximation, the corrector strengths follow Simpson's Rule, forming an accurate quasi-local canceling approximation to the nonlinearity. The F, C, and D correctors may also be used to obtain precise control of the horizontal, coupled, and vertical motion. Correction by three or more orders of magnitude can be obtained, and simple solutions to a fundamental problem in beam transport have been obtained. 13 refs., 1 fig., 1 tab

  12. A Linearized Relaxing Algorithm for the Specific Nonlinear Optimization Problem

    Directory of Open Access Journals (Sweden)

    Mio Horai

    2016-01-01

    Full Text Available We propose a new method for the specific nonlinear and nonconvex global optimization problem by using a linear relaxation technique. To simplify the specific nonlinear and nonconvex optimization problem, we transform the problem to the lower linear relaxation form, and we solve the linear relaxation optimization problem by the Branch and Bound Algorithm. Under some reasonable assumptions, the global convergence of the algorithm is certified for the problem. Numerical results show that this method is more efficient than the previous methods.

  13. Cross-constrained problems for nonlinear Schrodinger equation with harmonic potential

    Directory of Open Access Journals (Sweden)

    Runzhang Xu

    2012-11-01

    Full Text Available This article studies a nonlinear Schodinger equation with harmonic potential by constructing different cross-constrained problems. By comparing the different cross-constrained problems, we derive different sharp criterion and different invariant manifolds that separate the global solutions and blowup solutions. Moreover, we conclude that some manifolds are empty due to the essence of the cross-constrained problems. Besides, we compare the three cross-constrained problems and the three depths of the potential wells. In this way, we explain the gaps in [J. Shu and J. Zhang, Nonlinear Shrodinger equation with harmonic potential, Journal of Mathematical Physics, 47, 063503 (2006], which was pointed out in [R. Xu and Y. Liu, Remarks on nonlinear Schrodinger equation with harmonic potential, Journal of Mathematical Physics, 49, 043512 (2008].

  14. Introduction to nonlinear finite element analysis

    CERN Document Server

    Kim, Nam-Ho

    2015-01-01

    This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: ·         Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems ·         Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory ·    ...

  15. Genetic Algorithm for Mixed Integer Nonlinear Bilevel Programming and Applications in Product Family Design

    OpenAIRE

    Chenlu Miao; Gang Du; Yi Xia; Danping Wang

    2016-01-01

    Many leader-follower relationships exist in product family design engineering problems. We use bilevel programming (BLP) to reflect the leader-follower relationship and describe such problems. Product family design problems have unique characteristics; thus, mixed integer nonlinear BLP (MINLBLP), which has both continuous and discrete variables and multiple independent lower-level problems, is widely used in product family optimization. However, BLP is difficult in theory and is an NP-hard pr...

  16. Geometric Programming Approach to an Interactive Fuzzy Inventory Problem

    Directory of Open Access Journals (Sweden)

    Nirmal Kumar Mandal

    2011-01-01

    Full Text Available An interactive multiobjective fuzzy inventory problem with two resource constraints is presented in this paper. The cost parameters and index parameters, the storage space, the budgetary cost, and the objective and constraint goals are imprecise in nature. These parameters and objective goals are quantified by linear/nonlinear membership functions. A compromise solution is obtained by geometric programming method. If the decision maker is not satisfied with this result, he/she may try to update the current solution to his/her satisfactory solution. In this way we implement man-machine interactive procedure to solve the problem through geometric programming method.

  17. A demonstration of the improved efficiency of the canonical coordinates method using nonlinear combined heat and power economic dispatch problems

    Science.gov (United States)

    Chang, Hung-Chieh; Lin, Pei-Chun

    2014-02-01

    Economic dispatch is the short-term determination of the optimal output from a number of electricity generation facilities to meet the system load while providing power. As such, it represents one of the main optimization problems in the operation of electrical power systems. This article presents techniques to substantially improve the efficiency of the canonical coordinates method (CCM) algorithm when applied to nonlinear combined heat and power economic dispatch (CHPED) problems. The improvement is to eliminate the need to solve a system of nonlinear differential equations, which appears in the line search process in the CCM algorithm. The modified algorithm was tested and the analytical solution was verified using nonlinear CHPED optimization problems, thereby demonstrating the effectiveness of the algorithm. The CCM methods proved numerically stable and, in the case of nonlinear programs, produced solutions with unprecedented accuracy within a reasonable time.

  18. Renormgroup symmetries in problems of nonlinear geometrical optics

    International Nuclear Information System (INIS)

    Kovalev, V.F.

    1996-01-01

    Utilization and further development of the previously announced approach [1,2] enables one to construct renormgroup symmetries for a boundary value problem for the system of equations which describes propagation of a powerful radiation in a nonlinear medium in geometrical optics approximation. With the help of renormgroup symmetries new rigorous and approximate analytical solutions of nonlinear geometrical optics equations are obtained. Explicit analytical expressions are presented that characterize spatial evolution of laser beam which has an arbitrary intensity dependence at the boundary of the nonlinear medium. (author)

  19. Mathematical programming methods for large-scale topology optimization problems

    DEFF Research Database (Denmark)

    Rojas Labanda, Susana

    for mechanical problems, but has rapidly extended to many other disciplines, such as fluid dynamics and biomechanical problems. However, the novelty and improvements of optimization methods has been very limited. It is, indeed, necessary to develop of new optimization methods to improve the final designs......, and at the same time, reduce the number of function evaluations. Nonlinear optimization methods, such as sequential quadratic programming and interior point solvers, have almost not been embraced by the topology optimization community. Thus, this work is focused on the introduction of this kind of second...... for the classical minimum compliance problem. Two of the state-of-the-art optimization algorithms are investigated and implemented for this structural topology optimization problem. A Sequential Quadratic Programming (TopSQP) and an interior point method (TopIP) are developed exploiting the specific mathematical...

  20. Renormalization-group approach to nonlinear radiation-transport problems

    International Nuclear Information System (INIS)

    Chapline, G.F.

    1980-01-01

    A Monte Carlo method is derived for solving nonlinear radiation-transport problems that allows one to average over the effects of many photon absorptions and emissions at frequencies where the opacity is large. This method should allow one to treat radiation-transport problems with large optical depths, e.g., line-transport problems, with little increase in computational effort over that which is required for optically thin problems

  1. Parallel supercomputing: Advanced methods, algorithms, and software for large-scale linear and nonlinear problems

    Energy Technology Data Exchange (ETDEWEB)

    Carey, G.F.; Young, D.M.

    1993-12-31

    The program outlined here is directed to research on methods, algorithms, and software for distributed parallel supercomputers. Of particular interest are finite element methods and finite difference methods together with sparse iterative solution schemes for scientific and engineering computations of very large-scale systems. Both linear and nonlinear problems will be investigated. In the nonlinear case, applications with bifurcation to multiple solutions will be considered using continuation strategies. The parallelizable numerical methods of particular interest are a family of partitioning schemes embracing domain decomposition, element-by-element strategies, and multi-level techniques. The methods will be further developed incorporating parallel iterative solution algorithms with associated preconditioners in parallel computer software. The schemes will be implemented on distributed memory parallel architectures such as the CRAY MPP, Intel Paragon, the NCUBE3, and the Connection Machine. We will also consider other new architectures such as the Kendall-Square (KSQ) and proposed machines such as the TERA. The applications will focus on large-scale three-dimensional nonlinear flow and reservoir problems with strong convective transport contributions. These are legitimate grand challenge class computational fluid dynamics (CFD) problems of significant practical interest to DOE. The methods developed and algorithms will, however, be of wider interest.

  2. Numerical methods for solution of some nonlinear problems of mathematical physics

    International Nuclear Information System (INIS)

    Zhidkov, E.P.

    1981-01-01

    The continuous analog of the Newton method and its application to some nonlinear problems of mathematical physics using a computer is considered. It is shown that the application of this method in JINR to the wide range of nonlinear problems has shown its universality and high efficiency [ru

  3. Morozov-type discrepancy principle for nonlinear ill-posed problems ...

    Indian Academy of Sciences (India)

    For proving the existence of a regularization parameter under a Morozov-type discrepancy principle for Tikhonov regularization of nonlinear ill-posed problems, it is required to impose additional nonlinearity assumptions on the forward operator. Lipschitz continuity of the Freéchet derivative and requirement of the Lipschitz ...

  4. Morozov-type discrepancy principle for nonlinear ill-posed problems ...

    Indian Academy of Sciences (India)

    2016-08-26

    Aug 26, 2016 ... For proving the existence of a regularization parameter under a Morozov-type discrepancy principle for Tikhonov regularization of nonlinear ill-posed problems, it is required to impose additional nonlinearity assumptions on the forward operator. Lipschitz continuity of the Freéchet derivative and requirement ...

  5. Global Optimization of Nonlinear Blend-Scheduling Problems

    Directory of Open Access Journals (Sweden)

    Pedro A. Castillo Castillo

    2017-04-01

    Full Text Available The scheduling of gasoline-blending operations is an important problem in the oil refining industry. This problem not only exhibits the combinatorial nature that is intrinsic to scheduling problems, but also non-convex nonlinear behavior, due to the blending of various materials with different quality properties. In this work, a global optimization algorithm is proposed to solve a previously published continuous-time mixed-integer nonlinear scheduling model for gasoline blending. The model includes blend recipe optimization, the distribution problem, and several important operational features and constraints. The algorithm employs piecewise McCormick relaxation (PMCR and normalized multiparametric disaggregation technique (NMDT to compute estimates of the global optimum. These techniques partition the domain of one of the variables in a bilinear term and generate convex relaxations for each partition. By increasing the number of partitions and reducing the domain of the variables, the algorithm is able to refine the estimates of the global solution. The algorithm is compared to two commercial global solvers and two heuristic methods by solving four examples from the literature. Results show that the proposed global optimization algorithm performs on par with commercial solvers but is not as fast as heuristic approaches.

  6. Initial boundary value problems of nonlinear wave equations in an exterior domain

    International Nuclear Information System (INIS)

    Chen Yunmei.

    1987-06-01

    In this paper, we investigate the existence and uniqueness of the global solutions to the initial boundary value problems of nonlinear wave equations in an exterior domain. When the space dimension n >= 3, the unique global solution of the above problem is obtained for small initial data, even if the nonlinear term is fully nonlinear and contains the unknown function itself. (author). 10 refs

  7. Some New Results in Astrophysical Problems of Nonlinear Theory of Radiative Transfer

    Science.gov (United States)

    Pikichyan, H. V.

    2017-07-01

    In the interpretation of the observed astrophysical spectra, a decisive role is related to nonlinear problems of radiative transfer, because the processes of multiple interactions of matter of cosmic medium with the exciting intense radiation ubiquitously occur in astrophysical objects, and in their vicinities. Whereas, the intensity of the exciting radiation changes the physical properties of the original medium, and itself was modified, simultaneously, in a self-consistent manner under its influence. In the present report, we show that the consistent application of the principle of invariance in the nonlinear problem of bilateral external illumination of a scattering/absorbing one-dimensional anisotropic medium of finite geometrical thickness allows for simplifications that were previously considered as a prerogative only of linear problems. The nonlinear problem is analyzed through the three methods of the principle of invariance: (i) an adding of layers, (ii) its limiting form, described by differential equations of invariant imbedding, and (iii) a transition to the, so-called, functional equations of the "Ambartsumyan's complete invariance". Thereby, as an alternative to the Boltzmann equation, a new type of equations, so-called "kinetic equations of equivalence", are obtained. By the introduction of new functions - the so-called "linear images" of solution of nonlinear problem of radiative transfer, the linear structure of the solution of the nonlinear problem under study is further revealed. Linear images allow to convert naturally the statistical characteristics of random walk of a "single quantum" or their "beam of unit intensity", as well as widely known "probabilistic interpretation of phenomena of transfer", to the field of nonlinear problems. The structure of the equations obtained for determination of linear images is typical of linear problems.

  8. An iterative method for tri-level quadratic fractional programming problems using fuzzy goal programming approach

    Science.gov (United States)

    Kassa, Semu Mitiku; Tsegay, Teklay Hailay

    2017-08-01

    Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of problems. In this paper, we investigate a tri-level programming problem with quadratic fractional objective functions at each of the three levels. A solution algorithm has been proposed by applying fuzzy goal programming approach and by reformulating the fractional constraints to equivalent but non-fractional non-linear constraints. Based on the transformed formulation, an iterative procedure is developed that can yield a satisfactory solution to the tri-level problem. The numerical results on various illustrative examples demonstrated that the proposed algorithm is very much promising and it can also be used to solve larger-sized as well as n-level problems of similar structure.

  9. Parallel Solution of Robust Nonlinear Model Predictive Control Problems in Batch Crystallization

    Directory of Open Access Journals (Sweden)

    Yankai Cao

    2016-06-01

    Full Text Available Representing the uncertainties with a set of scenarios, the optimization problem resulting from a robust nonlinear model predictive control (NMPC strategy at each sampling instance can be viewed as a large-scale stochastic program. This paper solves these optimization problems using the parallel Schur complement method developed to solve stochastic programs on distributed and shared memory machines. The control strategy is illustrated with a case study of a multidimensional unseeded batch crystallization process. For this application, a robust NMPC based on min–max optimization guarantees satisfaction of all state and input constraints for a set of uncertainty realizations, and also provides better robust performance compared with open-loop optimal control, nominal NMPC, and robust NMPC minimizing the expected performance at each sampling instance. The performance of robust NMPC can be improved by generating optimization scenarios using Bayesian inference. With the efficient parallel solver, the solution time of one optimization problem is reduced from 6.7 min to 0.5 min, allowing for real-time application.

  10. SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis

    Energy Technology Data Exchange (ETDEWEB)

    Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

    1998-08-01

    This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. The notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.

  11. Interval Solution for Nonlinear Programming of Maximizing the Fatigue Life of V-Belt under Polymorphic Uncertain Environment

    Directory of Open Access Journals (Sweden)

    Zhong Wan

    2013-01-01

    Full Text Available In accord with the practical engineering design conditions, a nonlinear programming model is constructed for maximizing the fatigue life of V-belt drive in which some polymorphic uncertainties are incorporated. For a given satisfaction level and a confidence level, an equivalent formulation of this uncertain optimization model is obtained where only interval parameters are involved. Based on the concepts of maximal and minimal range inequalities for describing interval inequality, the interval parameter model is decomposed into two standard nonlinear programming problems, and an algorithm, called two-step based sampling algorithm, is developed to find an interval optimal solution for the original problem. Case study is employed to demonstrate the validity and practicability of the constructed model and the algorithm.

  12. Linear differential equations to solve nonlinear mechanical problems: A novel approach

    OpenAIRE

    Nair, C. Radhakrishnan

    2004-01-01

    Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential equation is known. Using the known solution of the non-linear differential equation, linear differential equations are set up. The solutions of these linear differential equations are found using standard techniques. Then the solutions of the linear differe...

  13. Implicit solvers for large-scale nonlinear problems

    International Nuclear Information System (INIS)

    Keyes, David E; Reynolds, Daniel R; Woodward, Carol S

    2006-01-01

    Computational scientists are grappling with increasingly complex, multi-rate applications that couple such physical phenomena as fluid dynamics, electromagnetics, radiation transport, chemical and nuclear reactions, and wave and material propagation in inhomogeneous media. Parallel computers with large storage capacities are paving the way for high-resolution simulations of coupled problems; however, hardware improvements alone will not prove enough to enable simulations based on brute-force algorithmic approaches. To accurately capture nonlinear couplings between dynamically relevant phenomena, often while stepping over rapid adjustments to quasi-equilibria, simulation scientists are increasingly turning to implicit formulations that require a discrete nonlinear system to be solved for each time step or steady state solution. Recent advances in iterative methods have made fully implicit formulations a viable option for solution of these large-scale problems. In this paper, we overview one of the most effective iterative methods, Newton-Krylov, for nonlinear systems and point to software packages with its implementation. We illustrate the method with an example from magnetically confined plasma fusion and briefly survey other areas in which implicit methods have bestowed important advantages, such as allowing high-order temporal integration and providing a pathway to sensitivity analyses and optimization. Lastly, we overview algorithm extensions under development motivated by current SciDAC applications

  14. Response of Non-Linear Shock Absorbers-Boundary Value Problem Analysis

    Science.gov (United States)

    Rahman, M. A.; Ahmed, U.; Uddin, M. S.

    2013-08-01

    A nonlinear boundary value problem of two degrees-of-freedom (DOF) untuned vibration damper systems using nonlinear springs and dampers has been numerically studied. As far as untuned damper is concerned, sixteen different combinations of linear and nonlinear springs and dampers have been comprehensively analyzed taking into account transient terms. For different cases, a comparative study is made for response versus time for different spring and damper types at three important frequency ratios: one at r = 1, one at r > 1 and one at r <1. The response of the system is changed because of the spring and damper nonlinearities; the change is different for different cases. Accordingly, an initially stable absorber may become unstable with time and vice versa. The analysis also shows that higher nonlinearity terms make the system more unstable. Numerical simulation includes transient vibrations. Although problems are much more complicated compared to those for a tuned absorber, a comparison of the results generated by the present numerical scheme with the exact one shows quite a reasonable agreement

  15. Assessment of non-linear analysis finite element program (NONSAP) for inelastic analysis

    International Nuclear Information System (INIS)

    Chang, T.Y.; Prachuktam, S.; Reich, M.

    1976-11-01

    An assessment on a nonlinear structural analysis finite element program called NONSAP is given with respect to its inelastic analysis capability for pressure vessels and components. The assessment was made from the review of its theoretical basis and bench mark problem runs. It was found that NONSAP has only limited capability for inelastic analysis. However, the program was written flexible enough that it can be easily extended or modified to suit the user's need. Moreover, some of the numerical difficulties in using NONSAP are pointed out

  16. Stochastic Fractional Programming Approach to a Mean and Variance Model of a Transportation Problem

    Directory of Open Access Journals (Sweden)

    V. Charles

    2011-01-01

    Full Text Available In this paper, we propose a stochastic programming model, which considers a ratio of two nonlinear functions and probabilistic constraints. In the former, only expected model has been proposed without caring variability in the model. On the other hand, in the variance model, the variability played a vital role without concerning its counterpart, namely, the expected model. Further, the expected model optimizes the ratio of two linear cost functions where as variance model optimize the ratio of two non-linear functions, that is, the stochastic nature in the denominator and numerator and considering expectation and variability as well leads to a non-linear fractional program. In this paper, a transportation model with stochastic fractional programming (SFP problem approach is proposed, which strikes the balance between previous models available in the literature.

  17. Non-linear analytic and coanalytic problems (Lp-theory, Clifford analysis, examples)

    International Nuclear Information System (INIS)

    Dubinskii, Yu A; Osipenko, A S

    2000-01-01

    Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the 'orthogonal' sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented

  18. 96 International Conference on Nonlinear Programming

    CERN Document Server

    1998-01-01

    About 60 scientists and students attended the 96' International Conference on Nonlinear Programming, which was held September 2-5 at Institute of Compu­ tational Mathematics and Scientific/Engineering Computing (ICMSEC), Chi­ nese Academy of Sciences, Beijing, China. 25 participants were from outside China and 35 from China. The conference was to celebrate the 60's birthday of Professor M.J.D. Powell (Fellow of Royal Society, University of Cambridge) for his many contributions to nonlinear optimization. On behalf of the Chinese Academy of Sciences, vice president Professor Zhi­ hong Xu attended the opening ceremony of the conference to express his warm welcome to all the participants. After the opening ceremony, Professor M.J.D. Powell gave the keynote lecture "The use of band matrices for second derivative approximations in trust region methods". 13 other invited lectures on recent advances of nonlinear programming were given during the four day meeting: "Primal-dual methods for nonconvex optimization" by...

  19. Morozov-type discrepancy principle for nonlinear ill-posed problems ...

    Indian Academy of Sciences (India)

    [3] Engl H W, Kunisch K and Neubauer A, Convergence rates for Tikhonov regularization of nonliner problems, Inverse Problems 5 (1989) 523–540. [4] Hanke M, Neubauer A and Scherzer O, A convergence analysis of Landweber iteration for nonlinear ill-posed problems, Numer. Math. 72 (1995) 21–37. [5] Hofmann B and ...

  20. Nonlinear problems in theoretical physics

    International Nuclear Information System (INIS)

    Ranada, A.F.

    1979-01-01

    This volume contains the lecture notes and review talks delivered at the 9th GIFT international seminar on theoretical physics on the general subject 'Nonlinear Problems in Theoretical Physics'. Mist contributions deal with recent developments in the theory of the spectral transformation and solitons, but there are also articles from the field of transport theory and plasma physics and an unconventional view of classical and quantum electrodynamics. All contributions to this volume will appear under their corresponding subject categories. (HJ)

  1. Studies in nonlinear problems of energy

    Energy Technology Data Exchange (ETDEWEB)

    Matkowsky, B.J.

    1992-07-01

    Emphasis has been on combustion and flame propagation. The research program was on modeling, analysis and computation of combustion phenomena, with emphasis on transition from laminar to turbulent combustion. Nonlinear dynamics and pattern formation were investigated in the transition. Stability of combustion waves, and transitions to complex waves are described. Combustion waves possess large activation energies, so that chemical reactions are significant only in thin layers, or reaction zones. In limit of infinite activation energy, the zones shrink to moving surfaces, (fronts) which must be found during the analysis, so that (moving free boundary problems). The studies are carried out for limiting case with fronts, while the numerical studies are carried out for finite, though large, activation energy. Accurate resolution of the solution in the reaction zones is essential, otherwise false predictions of dynamics are possible. Since the the reaction zones move, adaptive pseudo-spectral methods were developed. The approach is based on a synergism of analytical and computational methods. The numerical computations build on and extend the analytical information. Furthermore, analytical solutions serve as benchmarks for testing the accuracy of the computation. Finally, ideas from analysis (singular perturbation theory) have induced new approaches to computations. The computational results suggest new analysis to be considered. Among the recent interesting results, was spatio-temporal chaos in combustion. One goal is extension of the adaptive pseudo-spectral methods to adaptive domain decomposition methods. Efforts have begun to develop such methods for problems with multiple reaction zones, corresponding to problems with more complex, and more realistic chemistry. Other topics included stochastics, oscillators, Rysteretic Josephson junctions, DC SQUID, Markov jumps, laser with saturable absorber, chemical physics, Brownian movement, combustion synthesis, etc.

  2. On a non-linear pseudodifferential boundary value problem

    International Nuclear Information System (INIS)

    Nguyen Minh Chuong.

    1989-12-01

    A pseudodifferential boundary value problem for operators with symbols taking values in Sobolev spaces and with non-linear right-hand side was studied. Existence and uniqueness theorems were proved. (author). 11 refs

  3. Simultaneous multigrid techniques for nonlinear eigenvalue problems: Solutions of the nonlinear Schrödinger-Poisson eigenvalue problem in two and three dimensions

    Science.gov (United States)

    Costiner, Sorin; Ta'asan, Shlomo

    1995-07-01

    Algorithms for nonlinear eigenvalue problems (EP's) often require solving self-consistently a large number of EP's. Convergence difficulties may occur if the solution is not sought in an appropriate region, if global constraints have to be satisfied, or if close or equal eigenvalues are present. Multigrid (MG) algorithms for nonlinear problems and for EP's obtained from discretizations of partial differential EP have often been shown to be more efficient than single level algorithms. This paper presents MG techniques and a MG algorithm for nonlinear Schrödinger Poisson EP's. The algorithm overcomes the above mentioned difficulties combining the following techniques: a MG simultaneous treatment of the eigenvectors and nonlinearity, and with the global constrains; MG stable subspace continuation techniques for the treatment of nonlinearity; and a MG projection coupled with backrotations for separation of solutions. These techniques keep the solutions in an appropriate region, where the algorithm converges fast, and reduce the large number of self-consistent iterations to only a few or one MG simultaneous iteration. The MG projection makes it possible to efficiently overcome difficulties related to clusters of close and equal eigenvalues. Computational examples for the nonlinear Schrödinger-Poisson EP in two and three dimensions, presenting special computational difficulties that are due to the nonlinearity and to the equal and closely clustered eigenvalues are demonstrated. For these cases, the algorithm requires O(qN) operations for the calculation of q eigenvectors of size N and for the corresponding eigenvalues. One MG simultaneous cycle per fine level was performed. The total computational cost is equivalent to only a few Gauss-Seidel relaxations per eigenvector. An asymptotic convergence rate of 0.15 per MG cycle is attained.

  4. LDRD report nonlinear model reduction

    Energy Technology Data Exchange (ETDEWEB)

    Segalman, D.; Heinstein, M.

    1997-09-01

    The very general problem of model reduction of nonlinear systems was made tractable by focusing on the very large subclass consisting of linear subsystems connected by nonlinear interfaces. Such problems constitute a large part of the nonlinear structural problems encountered in addressing the Sandia missions. A synthesis approach to this class of problems was developed consisting of: detailed modeling of the interface mechanics; collapsing the interface simulation results into simple nonlinear interface models; constructing system models by assembling model approximations of the linear subsystems and the nonlinear interface models. These system models, though nonlinear, would have very few degrees of freedom. A paradigm problem, that of machine tool vibration, was selected for application of the reduction approach outlined above. Research results achieved along the way as well as the overall modeling of a specific machine tool have been very encouraging. In order to confirm the interface models resulting from simulation, it was necessary to develop techniques to deduce interface mechanics from experimental data collected from the overall nonlinear structure. A program to develop such techniques was also pursued with good success.

  5. Nonlinear problems in fluid dynamics and inverse scattering: Nonlinear waves and inverse scattering

    Science.gov (United States)

    Ablowitz, Mark J.

    1994-12-01

    Research investigations involving the fundamental understanding and applications of nonlinear wave motion and related studies of inverse scattering and numerical computation have been carried out and a number of significant results have been obtained. A class of nonlinear wave equations which can be solved by the inverse scattering transform (IST) have been studied, including the Kadaomtsev-Petviashvili (KP) equation, the Davey-Stewartson equation, and the 2+1 Toda system. The solutions obtained by IST correspond to the Cauchy initial value problem with decaying initial data. We have also solved two important systems via the IST method: a 'Volterra' system in 2+1 dimensions and a new one dimensional nonlinear equation which we refer to as the Toda differential-delay equation. Research in computational chaos in moderate to long time numerical simulations continues.

  6. Adomian decomposition method for nonlinear Sturm-Liouville problems

    Directory of Open Access Journals (Sweden)

    Sennur Somali

    2007-09-01

    Full Text Available In this paper the Adomian decomposition method is applied to the nonlinear Sturm-Liouville problem-y" + y(tp=λy(t, y(t > 0, t ∈ I = (0, 1, y(0 = y(1 = 0, where p > 1 is a constant and λ > 0 is an eigenvalue parameter. Also, the eigenvalues and the behavior of eigenfuctions of the problem are demonstrated.

  7. Non-linear programming method in optimization of fast reactors

    International Nuclear Information System (INIS)

    Pavelesku, M.; Dumitresku, Kh.; Adam, S.

    1975-01-01

    Application of the non-linear programming methods on optimization of nuclear materials distribution in fast reactor is discussed. The programming task composition is made on the basis of the reactor calculation dependent on the fuel distribution strategy. As an illustration of this method application the solution of simple example is given. Solution of the non-linear program is done on the basis of the numerical method SUMT. (I.T.)

  8. Selected Problems in Nonlinear Dynamics and Sociophysics

    Science.gov (United States)

    Westley, Alexandra Renee

    This Ph.D. dissertation focuses on a collection of problems on the dynamical behavior of nonlinear many-body systems, drawn from two substantially different areas. First, the dynamical behavior seen in strongly nonlinear lattices such as in the Fermi-Pasta-Ulam-Tsingou (FPUT) system (part I) and second, time evolution behavior of interacting living objects which can be broadly considered as sociophysics systems (part II). The studies on FPUT-like systems will comprise of five chapters, dedicated to the properties of solitary and anti-solitary waves in the system, how localized nonlinear excitations decay and spread throughout these lattices, how two colliding solitary waves can precipitate highly localized and stable excitations, a possible alternative way to view these localized excitations through Duffing oscillators, and finally an exploration of parametric resonance in an FPUT-like lattice. Part II consists of two problems in the context of sociophysics. I use molecular dynamics inspired simulations to study the size and the stability of social groups of chimpanzees (such as those seen in central Africa) and compare the results with existing observations on the stability of chimpanzee societies. Secondly, I use an agent-based model to simulate land battles between an intelligent army and an insurgency when both have access to equally powerful weaponry. The study considers genetic algorithm based adaptive strategies to infer the strategies needed for the intelligent army to win the battles.

  9. Analytic approximations to nonlinear boundary value problems modeling beam-type nano-electromechanical systems

    Energy Technology Data Exchange (ETDEWEB)

    Zou, Li [Dalian Univ. of Technology, Dalian City (China). State Key Lab. of Structural Analysis for Industrial Equipment; Liang, Songxin; Li, Yawei [Dalian Univ. of Technology, Dalian City (China). School of Mathematical Sciences; Jeffrey, David J. [Univ. of Western Ontario, London (Canada). Dept. of Applied Mathematics

    2017-06-01

    Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.

  10. A new integrability theory for certain nonlinear physical problems

    International Nuclear Information System (INIS)

    Berger, M.S.

    1993-01-01

    A new mathematically sound integrability theory for certain nonlinear problems defined by ordinary or partial differential equations is defined. The new theory works in an arbitrary finite number of space dimensions. Moreover, if a system is integrable in the new sense described here, it has a remarkable stability property that distinguishes if from any previously known integrability ideas. The new theory proceeds by establishing a ''global normal form'' for the problem at hand. This normal form holds subject to canonical coordinate transformations, extending such classical ideas by using new nonlinear methods of infinite dimensional functional analysis. The global normal form in question is related to the mathematical theory of singularities of mappings of H. Whitney and R. Thom extended globally and form finite to infinite dimensions. Thus bifurcation phenomena are naturally included in the new integrability theory. Typical examples include the classically nonintegrable Riccati equation, certain non-Euclidean mean field theories, certain parabolic reaction diffusion equations and the hyperbolic nonlinear telegrapher's equation. (Author)

  11. Method for nonlinear exponential regression analysis

    Science.gov (United States)

    Junkin, B. G.

    1972-01-01

    Two computer programs developed according to two general types of exponential models for conducting nonlinear exponential regression analysis are described. Least squares procedure is used in which the nonlinear problem is linearized by expanding in a Taylor series. Program is written in FORTRAN 5 for the Univac 1108 computer.

  12. FATAL, General Experiment Fitting Program by Nonlinear Regression Method

    International Nuclear Information System (INIS)

    Salmon, L.; Budd, T.; Marshall, M.

    1982-01-01

    1 - Description of problem or function: A generalized fitting program with a free-format keyword interface to the user. It permits experimental data to be fitted by non-linear regression methods to any function describable by the user. The user requires the minimum of computer experience but needs to provide a subroutine to define his function. Some statistical output is included as well as 'best' estimates of the function's parameters. 2 - Method of solution: The regression method used is based on a minimization technique devised by Powell (Harwell Subroutine Library VA05A, 1972) which does not require the use of analytical derivatives. The method employs a quasi-Newton procedure balanced with a steepest descent correction. Experience shows this to be efficient for a very wide range of application. 3 - Restrictions on the complexity of the problem: The current version of the program permits functions to be defined with up to 20 parameters. The function may be fitted to a maximum of 400 points, preferably with estimated values of weight given

  13. Ultimate limit state design of sheet pile walls by finite elements and nonlinear programming

    DEFF Research Database (Denmark)

    Krabbenhøft, Kristian; Damkilde, Lars; Krabbenhøft, Sven

    2005-01-01

    The design of sheet pile walls by lower bound limit analysis is considered. The design problem involves the determination of the necessary yield moment of the wall, the wall depth and the anchor force such that the structure is able to sustain the given loads. This problem is formulated...... as a nonlinear programming problem where the yield moment of the wall is minimized subject to equilibrium and yield conditions. The finite element discretization used enables exact fulfillment of these conditions and thus, according to the lower bound theorem, the solutions are safe....

  14. Some nonlinear problems in the manipulation of beams

    International Nuclear Information System (INIS)

    Sessler, A.M.

    1990-01-01

    An overview is given of nonlinear problems that arise in the manipulation of beams. Beams can be made of material particles or photons, can be intense or dilute, can be energetic or not, and they can be propagating in vacuum or in a medium. The nonlinear aspects of the motion are different in each case, and this diversity of behavior is categorized. Many examples are given, which serves to illustrate the categorization and, furthermore, display the richness of behavior encountered in the physics of beams. 25 refs., 5 figs

  15. Non-linear analytic and coanalytic problems ( L_p-theory, Clifford analysis, examples)

    Science.gov (United States)

    Dubinskii, Yu A.; Osipenko, A. S.

    2000-02-01

    Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the "orthogonal" sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented.

  16. Solution of Contact Problems for Nonlinear Gao Beam and Obstacle

    Directory of Open Access Journals (Sweden)

    J. Machalová

    2015-01-01

    Full Text Available Contact problem for a large deformed beam with an elastic obstacle is formulated, analyzed, and numerically solved. The beam model is governed by a nonlinear fourth-order differential equation developed by Gao, while the obstacle is considered as the elastic foundation of Winkler’s type in some distance under the beam. The problem is static without a friction and modeled either using Signorini conditions or by means of normal compliance contact conditions. The problems are then reformulated as optimal control problems which is useful both for theoretical aspects and for solution methods. Discretization is based on using the mixed finite element method with independent discretization and interpolations for foundation and beam elements. Numerical examples demonstrate usefulness of the presented solution method. Results for the nonlinear Gao beam are compared with results for the classical Euler-Bernoulli beam model.

  17. A fast nonlinear conjugate gradient based method for 3D frictional contact problems

    NARCIS (Netherlands)

    Zhao, J.; Vollebregt, E.A.H.; Oosterlee, C.W.

    2014-01-01

    This paper presents a fast numerical solver for a nonlinear constrained optimization problem, arising from a 3D frictional contact problem. It incorporates an active set strategy with a nonlinear conjugate gradient method. One novelty is to consider the tractions of each slip element in a polar

  18. The Cauchy problem for non-linear Klein-Gordon equations

    International Nuclear Information System (INIS)

    Simon, J.C.H.; Taflin, E.

    1993-01-01

    We consider in R n+1 , n≥2, the non-linear Klein-Gordon equation. We prove for such an equation that there is neighbourhood of zero in a Hilbert space of initial conditions for which the Cauchy problem has global solutions and on which there is asymptotic completeness. The inverse of the wave operator linearizes the non-linear equation. If, moreover, the equation is manifestly Poincare covariant then the non-linear representation of the Poincare-Lie algebra, associated with the non-linear Klein-Gordon equation is integrated to a non-linear representation of the Poincare group on an invariant neighbourhood of zero in the Hilbert space. This representation is linearized by the inverse of the wave operator. The Hilbert space is, in both cases, the closure of the space of the differentiable vectors for the linear representation of the Poincare group, associated with the Klein-Gordon equation, with respect to a norm defined by the representation of the enveloping algebra. (orig.)

  19. Intrinsic nonlinearity and method of disturbed observations in inverse problems of celestial mechanics

    Science.gov (United States)

    Avdyushev, Victor A.

    2017-12-01

    Orbit determination from a small sample of observations over a very short observed orbital arc is a strongly nonlinear inverse problem. In such problems an evaluation of orbital uncertainty due to random observation errors is greatly complicated, since linear estimations conventionally used are no longer acceptable for describing the uncertainty even as a rough approximation. Nevertheless, if an inverse problem is weakly intrinsically nonlinear, then one can resort to the so-called method of disturbed observations (aka observational Monte Carlo). Previously, we showed that the weaker the intrinsic nonlinearity, the more efficient the method, i.e. the more accurate it enables one to simulate stochastically the orbital uncertainty, while it is strictly exact only when the problem is intrinsically linear. However, as we ascertained experimentally, its efficiency was found to be higher than that of other stochastic methods widely applied in practice. In the present paper we investigate the intrinsic nonlinearity in complicated inverse problems of Celestial Mechanics when orbits are determined from little informative samples of observations, which typically occurs for recently discovered asteroids. To inquire into the question, we introduce an index of intrinsic nonlinearity. In asteroid problems it evinces that the intrinsic nonlinearity can be strong enough to affect appreciably probabilistic estimates, especially at the very short observed orbital arcs that the asteroids travel on for about a hundredth of their orbital periods and less. As it is known from regression analysis, the source of intrinsic nonlinearity is the nonflatness of the estimation subspace specified by a dynamical model in the observation space. Our numerical results indicate that when determining asteroid orbits it is actually very slight. However, in the parametric space the effect of intrinsic nonlinearity is exaggerated mainly by the ill-conditioning of the inverse problem. Even so, as for the

  20. On a Highly Nonlinear Self-Obstacle Optimal Control Problem

    Energy Technology Data Exchange (ETDEWEB)

    Di Donato, Daniela, E-mail: daniela.didonato@unitn.it [University of Trento, Department of Mathematics (Italy); Mugnai, Dimitri, E-mail: dimitri.mugnai@unipg.it [Università di Perugia, Dipartimento di Matematica e Informatica (Italy)

    2015-10-15

    We consider a non-quadratic optimal control problem associated to a nonlinear elliptic variational inequality, where the obstacle is the control itself. We show that, fixed a desired profile, there exists an optimal solution which is not far from it. Detailed characterizations of the optimal solution are given, also in terms of approximating problems.

  1. Experimental analysis of nonlinear problems in solid mechanics

    International Nuclear Information System (INIS)

    1982-01-01

    The booklet presents abstracts of papers from the Euromech Colloqium No. 152 held from Sept. 20th to 24th, 1982 in Wuppertal, Federal Republic of Germany. All the papers are dealing with Experimental Analysis of Nonlinear Problems in Solid Mechanics. (RW)

  2. Lectures on nonlinear evolution equations initial value problems

    CERN Document Server

    Racke, Reinhard

    2015-01-01

    This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behavior of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial-boundary value p...

  3. A nonsmooth nonlinear conjugate gradient method for interactive contact force problems

    DEFF Research Database (Denmark)

    Silcowitz, Morten; Abel, Sarah Maria Niebe; Erleben, Kenny

    2010-01-01

    of a nonlinear complementarity problem (NCP), which can be solved using an iterative splitting method, such as the projected Gauss–Seidel (PGS) method. We present a novel method for solving the NCP problem by applying a Fletcher–Reeves type nonlinear nonsmooth conjugate gradient (NNCG) type method. We analyze...... and present experimental convergence behavior and properties of the new method. Our results show that the NNCG method has at least the same convergence rate as PGS, and in many cases better....

  4. New Exact Penalty Functions for Nonlinear Constrained Optimization Problems

    Directory of Open Access Journals (Sweden)

    Bingzhuang Liu

    2014-01-01

    Full Text Available For two kinds of nonlinear constrained optimization problems, we propose two simple penalty functions, respectively, by augmenting the dimension of the primal problem with a variable that controls the weight of the penalty terms. Both of the penalty functions enjoy improved smoothness. Under mild conditions, it can be proved that our penalty functions are both exact in the sense that local minimizers of the associated penalty problem are precisely the local minimizers of the original constrained problem.

  5. Galerkin approximations of nonlinear optimal control problems in Hilbert spaces

    Directory of Open Access Journals (Sweden)

    Mickael D. Chekroun

    2017-07-01

    Full Text Available Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere $\\mathbb{S}^2$.

  6. Analytical vs. Simulation Solution Techniques for Pulse Problems in Non-linear Stochastic Dynamics

    DEFF Research Database (Denmark)

    Iwankiewicz, R.; Nielsen, Søren R. K.

    Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically-numerical tec......Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically...

  7. A fast nonlinear conjugate gradient based method for 3D concentrated frictional contact problems

    NARCIS (Netherlands)

    J. Zhao (Jing); E.A.H. Vollebregt (Edwin); C.W. Oosterlee (Cornelis)

    2015-01-01

    htmlabstractThis paper presents a fast numerical solver for a nonlinear constrained optimization problem, arising from 3D concentrated frictional shift and rolling contact problems with dry Coulomb friction. The solver combines an active set strategy with a nonlinear conjugate gradient method. One

  8. The nurse scheduling problem: a goal programming and nonlinear optimization approaches

    Science.gov (United States)

    Hakim, L.; Bakhtiar, T.; Jaharuddin

    2017-01-01

    Nurses scheduling is an activity of allocating nurses to conduct a set of tasks at certain room at a hospital or health centre within a certain period. One of obstacles in the nurse scheduling is the lack of resources in order to fulfil the needs of the hospital. Nurse scheduling which is undertaken manually will be at risk of not fulfilling some nursing rules set by the hospital. Therefore, this study aimed to perform scheduling models that satisfy all the specific rules set by the management of Bogor State Hospital. We have developed three models to overcome the scheduling needs. Model 1 is designed to schedule nurses who are solely assigned to a certain inpatient unit and Model 2 is constructed to manage nurses who are assigned to an inpatient room as well as at Polyclinic room as conjunct nurses. As the assignment of nurses on each shift is uneven, then we propose Model 3 to minimize the variance of the workload in order to achieve equitable assignment on every shift. The first two models are formulated in goal programming framework, while the last model is in nonlinear optimization form.

  9. On the solvability of initial boundary value problems for nonlinear ...

    African Journals Online (AJOL)

    In this paper, we study the initial boundary value problems for a non-linear time dependent Schrödinger equation with Dirichlet and Neumann boundary conditions, respectively. We prove the existence and uniqueness of solutions of the initial boundary value problems by using Galerkin's method. Keywords: Initial boundary ...

  10. Possibility/Necessity-Based Probabilistic Expectation Models for Linear Programming Problems with Discrete Fuzzy Random Variables

    Directory of Open Access Journals (Sweden)

    Hideki Katagiri

    2017-10-01

    Full Text Available This paper considers linear programming problems (LPPs where the objective functions involve discrete fuzzy random variables (fuzzy set-valued discrete random variables. New decision making models, which are useful in fuzzy stochastic environments, are proposed based on both possibility theory and probability theory. In multi-objective cases, Pareto optimal solutions of the proposed models are newly defined. Computational algorithms for obtaining the Pareto optimal solutions of the proposed models are provided. It is shown that problems involving discrete fuzzy random variables can be transformed into deterministic nonlinear mathematical programming problems which can be solved through a conventional mathematical programming solver under practically reasonable assumptions. A numerical example of agriculture production problems is given to demonstrate the applicability of the proposed models to real-world problems in fuzzy stochastic environments.

  11. First international conference on nonlinear problems in aviation and aerospace

    International Nuclear Information System (INIS)

    Sivasundaram, S.

    1994-01-01

    The International Conference on Nonlinear Problems in Aviation and Aerospace was held at Embry-Riddle Aeronautical University, Daytona Beach, Florida on May 9-11, 1996. This conference was sponsored by the International Federation of Nonlinear Analysts, International Federation of Information Processing, and Embry-Riddle Aeronautical University. Over one hundred engineers, scientists, and mathematicians from seventeen countries attended. These proceedings include keynote addresses, invited lectures, and contributed papers presented during the conference

  12. Some problems on nonlinear hyperbolic equations and applications

    CERN Document Server

    Peng, YueJun

    2010-01-01

    This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications. It presents recent progress and results obtained in the domains related to both subjects without attaching much importance to the details of proofs but rather to difficulties encountered, to open problems and possible ways to be exploited. It will be very useful for promoting further study on some important problems in the future.

  13. From a Nonlinear, Nonconvex Variational Problem to a Linear, Convex Formulation

    International Nuclear Information System (INIS)

    Egozcue, J.; Meziat, R.; Pedregal, P.

    2002-01-01

    We propose a general approach to deal with nonlinear, nonconvex variational problems based on a reformulation of the problem resulting in an optimization problem with linear cost functional and convex constraints. As a first step we explicitly explore these ideas to some one-dimensional variational problems and obtain specific conclusions of an analytical and numerical nature

  14. Nonlinear reaction-diffusion equations with delay: some theorems, test problems, exact and numerical solutions

    Science.gov (United States)

    Polyanin, A. D.; Sorokin, V. G.

    2017-12-01

    The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.

  15. JAC2D: A two-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method

    International Nuclear Information System (INIS)

    Biffle, J.H.; Blanford, M.L.

    1994-05-01

    JAC2D is a two-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equations. The method is implemented in a two-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. A four-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic/plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere

  16. JAC3D -- A three-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method

    International Nuclear Information System (INIS)

    Biffle, J.H.

    1993-02-01

    JAC3D is a three-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equation. The method is implemented in a three-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. An eight-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic-plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere

  17. On Newton-Raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity

    Directory of Open Access Journals (Sweden)

    Koh Kim Jie

    2017-01-01

    Full Text Available Quadratic damping nonlinearity is challenging for displacement based structural dynamics problem as the problem is nonlinear in time derivative of the primitive variable. For such nonlinearity, the formulation of tangent stiffness matrix is not lucid in the literature. Consequently, ambiguity related to kinematics update arises when implementing the time integration-iterative algorithm. In present work, an Euler-Bernoulli beam vibration problem with quadratic damping nonlinearity is addressed as the main source of quadratic damping nonlinearity arises from drag force estimation, which is generally valid only for slender structures. Employing Newton-Raphson formulation, tangent stiffness components associated with quadratic damping nonlinearity requires velocity input for evaluation purpose. For this reason, two mathematically equivalent algorithm structures with different kinematics arrangement are tested. Both algorithm structures result in the same accuracy and convergence characteristic of solution.

  18. Development of nonlinear dynamic analysis program for nuclear piping systems

    International Nuclear Information System (INIS)

    Kamichika, Ryoichi; Izawa, Masahiro; Yamadera, Masao

    1980-01-01

    In the design for nuclear power piping, pipe-whip protection shall be considered in order to keep the function of safety related system even when postulated piping rupture occurs. This guideline was shown in U.S. Regulatory Guide 1.46 for the first time and has been applied in Japanese nuclear power plants. In order to analyze the dynamic behavior followed by pipe rupture, nonlinear analysis is required for the piping system including restraints which play the role of an energy absorber. REAPPS (Rupture Effective Analysis of Piping Systems) has been developed for this purpose. This program can be applied to general piping systems having branches etc. Pre- and post- processors are prepared in this program in order to easily input the data for the piping engineer and show the results optically by use of a graphic display respectively. The piping designer can easily solve many problems in his daily work by use of this program. This paper describes about the theoretical background and functions of this program and shows some examples. (author)

  19. Arbitrary Lagrangian-Eulerian method for non-linear problems of geomechanics

    International Nuclear Information System (INIS)

    Nazem, M; Carter, J P; Airey, D W

    2010-01-01

    In many geotechnical problems it is vital to consider the geometrical non-linearity caused by large deformation in order to capture a more realistic model of the true behaviour. The solutions so obtained should then be more accurate and reliable, which should ultimately lead to cheaper and safer design. The Arbitrary Lagrangian-Eulerian (ALE) method originated from fluid mechanics, but has now been well established for solving large deformation problems in geomechanics. This paper provides an overview of the ALE method and its challenges in tackling problems involving non-linearities due to material behaviour, large deformation, changing boundary conditions and time-dependency, including material rate effects and inertia effects in dynamic loading applications. Important aspects of ALE implementation into a finite element framework will also be discussed. This method is then employed to solve some interesting and challenging geotechnical problems such as the dynamic bearing capacity of footings on soft soils, consolidation of a soil layer under a footing, and the modelling of dynamic penetration of objects into soil layers.

  20. Consensus problem in directed networks of multi-agents via nonlinear protocols

    International Nuclear Information System (INIS)

    Liu Xiwei; Chen Tianping; Lu Wenlian

    2009-01-01

    In this Letter, the consensus problem via distributed nonlinear protocols for directed networks is investigated. Its dynamical behaviors are described by ordinary differential equations (ODEs). Based on graph theory, matrix theory and the Lyapunov direct method, some sufficient conditions of nonlinear protocols guaranteeing asymptotical or exponential consensus are presented and rigorously proved. The main contribution of this work is that for nonlinearly coupled networks, we generalize the results for undirected networks to directed networks. Consensus under pinning control technique is also developed here. Simulations are also given to show the validity of the theories.

  1. Inverse Boundary Value Problem for Non-linear Hyperbolic Partial Differential Equations

    OpenAIRE

    Nakamura, Gen; Vashisth, Manmohan

    2017-01-01

    In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\\geq 3$. This non-linear wave equation has a trivial solution, i.e. zero solution. By linearizing this equation at the trivial solution, we have the usual linear isotropic wave equation with the speed $\\sqrt{\\gamma(x)}$ at each point $x$ in a given spacial domain. For any small solution $u=u(t,x)$ of this non-linear equation, we have the linear isotr...

  2. Asymptotics for inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Kaikina, Elena I., E-mail: ekaikina@matmor.unam.mx [Centro de Ciencias Matemáticas, UNAM Campus Morelia, AP 61-3 (Xangari), Morelia CP 58089, Michoacán (Mexico)

    2013-11-15

    We consider the inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation, formulated on a half-line. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time.

  3. Asymptotics for inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation

    International Nuclear Information System (INIS)

    Kaikina, Elena I.

    2013-01-01

    We consider the inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation, formulated on a half-line. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time

  4. Application of HPEM to investigate the response and stability of nonlinear problems in vibration

    DEFF Research Database (Denmark)

    Mohammadi, M.H.; Mohammadi, A.; Kimiaeifar, A.

    2010-01-01

    In this work, a powerful analytical method, called He's Parameter Expanding Methods (HPEM) is used to obtain the exact solution of nonlinear problems in nonlinear vibration. In this work, the governing equation is obtained by using Lagrange method, then the nonlinear governing equation is solved...

  5. On discrete maximum principles for nonlinear elliptic problems

    Czech Academy of Sciences Publication Activity Database

    Karátson, J.; Korotov, S.; Křížek, Michal

    2007-01-01

    Roč. 76, č. 1 (2007), s. 99-108 ISSN 0378-4754 R&D Projects: GA MŠk 1P05ME749; GA AV ČR IAA1019201 Institutional research plan: CEZ:AV0Z10190503 Keywords : nonlinear elliptic problem * mixed boundary conditions * finite element method Subject RIV: BA - General Mathematics Impact factor: 0.738, year: 2007

  6. Policy Iteration for $H_\\infty $ Optimal Control of Polynomial Nonlinear Systems via Sum of Squares Programming.

    Science.gov (United States)

    Zhu, Yuanheng; Zhao, Dongbin; Yang, Xiong; Zhang, Qichao

    2018-02-01

    Sum of squares (SOS) polynomials have provided a computationally tractable way to deal with inequality constraints appearing in many control problems. It can also act as an approximator in the framework of adaptive dynamic programming. In this paper, an approximate solution to the optimal control of polynomial nonlinear systems is proposed. Under a given attenuation coefficient, the Hamilton-Jacobi-Isaacs equation is relaxed to an optimization problem with a set of inequalities. After applying the policy iteration technique and constraining inequalities to SOS, the optimization problem is divided into a sequence of feasible semidefinite programming problems. With the converged solution, the attenuation coefficient is further minimized to a lower value. After iterations, approximate solutions to the smallest -gain and the associated optimal controller are obtained. Four examples are employed to verify the effectiveness of the proposed algorithm.

  7. A novel approach based on preference-based index for interval bilevel linear programming problem.

    Science.gov (United States)

    Ren, Aihong; Wang, Yuping; Xue, Xingsi

    2017-01-01

    This paper proposes a new methodology for solving the interval bilevel linear programming problem in which all coefficients of both objective functions and constraints are considered as interval numbers. In order to keep as much uncertainty of the original constraint region as possible, the original problem is first converted into an interval bilevel programming problem with interval coefficients in both objective functions only through normal variation of interval number and chance-constrained programming. With the consideration of different preferences of different decision makers, the concept of the preference level that the interval objective function is preferred to a target interval is defined based on the preference-based index. Then a preference-based deterministic bilevel programming problem is constructed in terms of the preference level and the order relation [Formula: see text]. Furthermore, the concept of a preference δ -optimal solution is given. Subsequently, the constructed deterministic nonlinear bilevel problem is solved with the help of estimation of distribution algorithm. Finally, several numerical examples are provided to demonstrate the effectiveness of the proposed approach.

  8. A novel approach based on preference-based index for interval bilevel linear programming problem

    Directory of Open Access Journals (Sweden)

    Aihong Ren

    2017-05-01

    Full Text Available Abstract This paper proposes a new methodology for solving the interval bilevel linear programming problem in which all coefficients of both objective functions and constraints are considered as interval numbers. In order to keep as much uncertainty of the original constraint region as possible, the original problem is first converted into an interval bilevel programming problem with interval coefficients in both objective functions only through normal variation of interval number and chance-constrained programming. With the consideration of different preferences of different decision makers, the concept of the preference level that the interval objective function is preferred to a target interval is defined based on the preference-based index. Then a preference-based deterministic bilevel programming problem is constructed in terms of the preference level and the order relation ⪯ m w $\\preceq_{mw}$ . Furthermore, the concept of a preference δ-optimal solution is given. Subsequently, the constructed deterministic nonlinear bilevel problem is solved with the help of estimation of distribution algorithm. Finally, several numerical examples are provided to demonstrate the effectiveness of the proposed approach.

  9. Assessment of Two Analytical Methods in Solving the Linear and Nonlinear Elastic Beam Deformation Problems

    DEFF Research Database (Denmark)

    Barari, Amin; Ganjavi, B.; Jeloudar, M. Ghanbari

    2010-01-01

    and fluid mechanics. Design/methodology/approach – Two new but powerful analytical methods, namely, He's VIM and HPM, are introduced to solve some boundary value problems in structural engineering and fluid mechanics. Findings – Analytical solutions often fit under classical perturbation methods. However......, as with other analytical techniques, certain limitations restrict the wide application of perturbation methods, most important of which is the dependence of these methods on the existence of a small parameter in the equation. Disappointingly, the majority of nonlinear problems have no small parameter at all......Purpose – In the last two decades with the rapid development of nonlinear science, there has appeared ever-increasing interest of scientists and engineers in the analytical techniques for nonlinear problems. This paper considers linear and nonlinear systems that are not only regarded as general...

  10. On some nonlinear problems arising in the physics of ionized gases

    International Nuclear Information System (INIS)

    Hilhorst-Goldman, D.

    1981-01-01

    The author reports results obtained by rigorous analysis of a nonlinear differential equation for the electron density nsub(e) in a specific type of electrical discharge. The problem is essentially two-dimensional. She discusses in particular the escape of electrons to infinity above a critical temperature and the boundary layer exhibited by nsub(e) near zero temperature. A singular boundary value problem arising in a pre-breakdown gas discharge is discussed. A Coulomb gas is considered in a special experimental situation: the pre-breakdown gas discharge between two electrodes. The equation for the negative charge density can be formulated as a nonlinear parabolic equation degenerate at the origin. The existence and uniqueness of the solution are proved as well as the asymptotic stability of its unique steady state. Some results are also given about the rate of convergence. The variational characterisation of the limit solution of a singular perturbation problem and variational analysis of a perturbed free boundary problem are considered. (Auth./C.F.)

  11. Linear combination of forecasts with numerical adjustment via MINIMAX non-linear programming

    Directory of Open Access Journals (Sweden)

    Jairo Marlon Corrêa

    2016-03-01

    Full Text Available This paper proposes a linear combination of forecasts obtained from three forecasting methods (namely, ARIMA, Exponential Smoothing and Artificial Neural Networks whose adaptive weights are determined via a multi-objective non-linear programming problem, which seeks to minimize, simultaneously, the statistics: MAE, MAPE and MSE. The results achieved by the proposed combination are compared with the traditional approach of linear combinations of forecasts, where the optimum adaptive weights are determined only by minimizing the MSE; with the combination method by arithmetic mean; and with individual methods

  12. Dynamics and vibrations progress in nonlinear analysis

    CERN Document Server

    Kachapi, Seyed Habibollah Hashemi

    2014-01-01

    Dynamical and vibratory systems are basically an application of mathematics and applied sciences to the solution of real world problems. Before being able to solve real world problems, it is necessary to carefully study dynamical and vibratory systems and solve all available problems in case of linear and nonlinear equations using analytical and numerical methods. It is of great importance to study nonlinearity in dynamics and vibration; because almost all applied processes act nonlinearly, and on the other hand, nonlinear analysis of complex systems is one of the most important and complicated tasks, especially in engineering and applied sciences problems. There are probably a handful of books on nonlinear dynamics and vibrations analysis. Some of these books are written at a fundamental level that may not meet ambitious engineering program requirements. Others are specialized in certain fields of oscillatory systems, including modeling and simulations. In this book, we attempt to strike a balance between th...

  13. Inverse periodic problem for the discrete approximation of the Schroedinger nonlinear equation

    International Nuclear Information System (INIS)

    Bogolyubov, N.N.; Prikarpatskij, A.K.; AN Ukrainskoj SSR, Lvov. Inst. Prikladnykh Problem Mekhaniki i Matematiki)

    1982-01-01

    The problem of numerical solution of the Schroedinger nonlinear equation (1) iPSIsub(t) = PSIsub(xx)+-2(PSI)sup(2)PSI. The numerical solution of nonlinear differential equation supposes its discrete approximation is required for the realization of the computer calculation process. Tor the equation (1) there exists the following discrete approximation by variable x(2) iPSIsub(n, t) = (PSIsub(n+1)-2PSIsub(n)+PSIsub(n-1))/(Δx)sup(2)+-(PSIsub(n))sup(2)(PSIsub(n+1)+PSIsub(n-1)), n=0, +-1, +-2... where PSIsub(n)(+) is the corresponding value of PSI(x, t) function in the node and divisions with the equilibrium step Δx. The main problem is obtaining analytically exact solutions of the equations (2). The analysis of the equation system (2) is performed on the base of the discrete analogue of the periodic variant of the inverse scattering problem method developed with the aid of nonlinear equations of the Korteweg-de Vries type. Obtained in explicit form are analytical solutions of the equations system (2). The solutions are expressed through the Riemann THETA-function [ru

  14. Multigrid techniques for nonlinear eigenvalue probems: Solutions of a nonlinear Schroedinger eigenvalue problem in 2D and 3D

    Science.gov (United States)

    Costiner, Sorin; Taasan, Shlomo

    1994-01-01

    This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.

  15. Application of the Green's function method to some nonlinear problems of an electron storage ring

    International Nuclear Information System (INIS)

    Kheifets, S.

    1984-01-01

    One of the most important characteristics of an electron storage ring is the size of the beam. However analytical calculations of beam size are beset with problems and the computational methods and programs which are used to overcome these are inadequate for all problems in which stochastic noise is an essential part. Two examples are, for an electron storage ring, beam-size evaluation including beam-beam interactions, and finding the beam size for a nonlinear machine. The method described should overcome some of the problems. It uses the Green's function method applied to the Fokker-Planck equation governing the distribution function in the phase space of particle motion. The new step is to consider the particle motion in two degrees of freedom rather than in one dimension. The technique is described fully and is then applied to a strong-focusing machine. (U.K.)

  16. Application of nonlinear Krylov acceleration to radiative transfer problems

    International Nuclear Information System (INIS)

    Till, A. T.; Adams, M. L.; Morel, J. E.

    2013-01-01

    The iterative solution technique used for radiative transfer is normally nested, with outer thermal iterations and inner transport iterations. We implement a nonlinear Krylov acceleration (NKA) method in the PDT code for radiative transfer problems that breaks nesting, resulting in more thermal iterations but significantly fewer total inner transport iterations. Using the metric of total inner transport iterations, we investigate a crooked-pipe-like problem and a pseudo-shock-tube problem. Using only sweep preconditioning, we compare NKA against a typical inner / outer method employing GMRES / Newton and find NKA to be comparable or superior. Finally, we demonstrate the efficacy of applying diffusion-based preconditioning to grey problems in conjunction with NKA. (authors)

  17. Analytical Solution of Nonlinear Problems in Classical Dynamics by Means of Lagrange-Ham

    DEFF Research Database (Denmark)

    Kimiaeifar, Amin; Mahdavi, S. H; Rabbani, A.

    2011-01-01

    In this work, a powerful analytical method, called Homotopy Analysis Methods (HAM) is coupled with Lagrange method to obtain the exact solution for nonlinear problems in classic dynamics. In this work, the governing equations are obtained by using Lagrange method, and then the nonlinear governing...

  18. The solution of a coupled system of nonlinear physical problems using the homotopy analysis method

    International Nuclear Information System (INIS)

    El-Wakil, S A; Abdou, M A

    2010-01-01

    In this article, the homotopy analysis method (HAM) has been applied to solve coupled nonlinear evolution equations in physics. The validity of this method has been successfully demonstrated by applying it to two nonlinear evolution equations, namely coupled nonlinear diffusion reaction equations and the (2+1)-dimensional Nizhnik-Novikov Veselov system. The results obtained by this method show good agreement with the ones obtained by other methods. The proposed method is a powerful and easy to use analytic tool for nonlinear problems and does not need small parameters in the equations. The HAM solutions contain an auxiliary parameter that provides a convenient way of controlling the convergence region of series solutions. The results obtained here reveal that the proposed method is very effective and simple for solving nonlinear evolution equations. The basic ideas of this approach can be widely employed to solve other strongly nonlinear problems.

  19. On the solution of nonconvex cardinality Boolean quadratic programming problems: a computational study

    KAUST Repository

    Lima, Ricardo

    2016-06-16

    This paper addresses the solution of a cardinality Boolean quadratic programming problem using three different approaches. The first transforms the original problem into six mixed-integer linear programming (MILP) formulations. The second approach takes one of the MILP formulations and relies on the specific features of an MILP solver, namely using starting incumbents, polishing, and callbacks. The last involves the direct solution of the original problem by solvers that can accomodate the nonlinear combinatorial problem. Particular emphasis is placed on the definition of the MILP reformulations and their comparison with the other approaches. The results indicate that the data of the problem has a strong influence on the performance of the different approaches, and that there are clear-cut approaches that are better for some instances of the data. A detailed analysis of the results is made to identify the most effective approaches for specific instances of the data. © 2016 Springer Science+Business Media New York

  20. On the solution of nonconvex cardinality Boolean quadratic programming problems: a computational study

    KAUST Repository

    Lima, Ricardo; Grossmann, Ignacio E.

    2016-01-01

    This paper addresses the solution of a cardinality Boolean quadratic programming problem using three different approaches. The first transforms the original problem into six mixed-integer linear programming (MILP) formulations. The second approach takes one of the MILP formulations and relies on the specific features of an MILP solver, namely using starting incumbents, polishing, and callbacks. The last involves the direct solution of the original problem by solvers that can accomodate the nonlinear combinatorial problem. Particular emphasis is placed on the definition of the MILP reformulations and their comparison with the other approaches. The results indicate that the data of the problem has a strong influence on the performance of the different approaches, and that there are clear-cut approaches that are better for some instances of the data. A detailed analysis of the results is made to identify the most effective approaches for specific instances of the data. © 2016 Springer Science+Business Media New York

  1. Some nonlinear space decomposition algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Tai, Xue-Cheng; Espedal, M. [Univ. of Bergen (Norway)

    1996-12-31

    Convergence of a space decomposition method is proved for a general convex programming problem. The space decomposition refers to methods that decompose a space into sums of subspaces, which could be a domain decomposition or a multigrid method for partial differential equations. Two algorithms are proposed. Both can be used for linear as well as nonlinear elliptic problems and they reduce to the standard additive and multiplicative Schwarz methods for linear elliptic problems. Two {open_quotes}hybrid{close_quotes} algorithms are also presented. They converge faster than the additive one and have better parallelism than the multiplicative method. Numerical tests with a two level domain decomposition for linear, nonlinear and interface elliptic problems are presented for the proposed algorithms.

  2. Explicit Nonlinear Model Predictive Control Theory and Applications

    CERN Document Server

    Grancharova, Alexandra

    2012-01-01

    Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø  Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...

  3. Nonlinear triple-point problems on time scales

    Directory of Open Access Journals (Sweden)

    Douglas R. Anderson

    2004-04-01

    Full Text Available We establish the existence of multiple positive solutions to the nonlinear second-order triple-point boundary-value problem on time scales, $$displaylines{ u^{Delta abla}(t+h(tf(t,u(t=0, cr u(a=alpha u(b+delta u^Delta(a,quad eta u(c+gamma u^Delta(c=0 }$$ for $tin[a,c]subsetmathbb{T}$, where $mathbb{T}$ is a time scale, $eta, gamma, deltage 0$ with $Beta+gamma>0$, $0

  4. Minimax terminal approach problem in two-level hierarchical nonlinear discrete-time dynamical system

    Energy Technology Data Exchange (ETDEWEB)

    Shorikov, A. F., E-mail: afshorikov@mail.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002, Russia Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990 (Russian Federation)

    2015-11-30

    We consider a discrete–time dynamical system consisting of three controllable objects. The motions of all objects are given by the corresponding vector nonlinear or linear discrete–time recurrent vector relations, and control system for its has two levels: basic (first or I level) that is dominating and subordinate level (second or II level) and both have different criterions of functioning and united a priori by determined informational and control connections defined in advance. For the dynamical system in question, we propose a mathematical formalization in the form of solving a multistep problem of two-level hierarchical minimax program control over the terminal approach process with incomplete information and give a general scheme for its solving.

  5. TENSOLVE: A software package for solving systems of nonlinear equations and nonlinear least squares problems using tensor methods

    Energy Technology Data Exchange (ETDEWEB)

    Bouaricha, A. [Argonne National Lab., IL (United States). Mathematics and Computer Science Div.; Schnabel, R.B. [Colorado Univ., Boulder, CO (United States). Dept. of Computer Science

    1996-12-31

    This paper describes a modular software package for solving systems of nonlinear equations and nonlinear least squares problems, using a new class of methods called tensor methods. It is intended for small to medium-sized problems, say with up to 100 equations and unknowns, in cases where it is reasonable to calculate the Jacobian matrix or approximate it by finite differences at each iteration. The software allows the user to select between a tensor method and a standard method based upon a linear model. The tensor method models F({ital x}) by a quadratic model, where the second-order term is chosen so that the model is hardly more expensive to form, store, or solve than the standard linear model. Moreover, the software provides two different global strategies, a line search and a two- dimensional trust region approach. Test results indicate that, in general, tensor methods are significantly more efficient and robust than standard methods on small and medium-sized problems in iterations and function evaluations.

  6. Multiple solutions for inhomogeneous nonlinear elliptic problems arising in astrophyiscs

    Directory of Open Access Journals (Sweden)

    Marco Calahorrano

    2004-04-01

    Full Text Available Using variational methods we prove the existence and multiplicity of solutions for some nonlinear inhomogeneous elliptic problems on a bounded domain in $mathbb{R}^n$, with $ngeq 2$ and a smooth boundary, and when the domain is $mathbb{R}_+^n$

  7. Lavrentiev regularization method for nonlinear ill-posed problems

    International Nuclear Information System (INIS)

    Kinh, Nguyen Van

    2002-10-01

    In this paper we shall be concerned with Lavientiev regularization method to reconstruct solutions x 0 of non ill-posed problems F(x)=y o , where instead of y 0 noisy data y δ is an element of X with absolut(y δ -y 0 ) ≤ δ are given and F:X→X is an accretive nonlinear operator from a real reflexive Banach space X into itself. In this regularization method solutions x α δ are obtained by solving the singularly perturbed nonlinear operator equation F(x)+α(x-x*)=y δ with some initial guess x*. Assuming certain conditions concerning the operator F and the smoothness of the element x*-x 0 we derive stability estimates which show that the accuracy of the regularized solutions is order optimal provided that the regularization parameter α has been chosen properly. (author)

  8. Iterative solution of a nonlinear system arising in phase change problems

    International Nuclear Information System (INIS)

    Williams, M.A.

    1987-01-01

    We consider several iterative methods for solving the nonlinear system arising from an enthalpy formulation of a phase change problem. We present the formulation of the problem. Implicit discretization of the governing equations results in a mildly nonlinear system at each time step. We discuss solving this system using Jacobi, Gauss-Seidel, and SOR iterations and a new modified preconditioned conjugate gradient (MPCG) algorithm. The new MPCG algorithm and its properties are discussed in detail. Numerical results are presented comparing the performance of the SOR algorithm and the MPCG algorithm with 1-step SSOR preconditioning. The MPCG algorithm exhibits a superlinear rate of convergence. The SOR algorithm exhibits a linear rate of convergence. Thus, the MPCG algorithm requires fewer iterations to converge than the SOR algorithm. However in most cases, the SOR algorithm requires less total computation time than the MPCG algorithm. Hence, the SOR algorithm appears to be more appropriate for the class of problems considered. 27 refs., 11 figs

  9. An Improved Search Approach for Solving Non-Convex Mixed-Integer Non Linear Programming Problems

    Science.gov (United States)

    Sitopu, Joni Wilson; Mawengkang, Herman; Syafitri Lubis, Riri

    2018-01-01

    The nonlinear mathematical programming problem addressed in this paper has a structure characterized by a subset of variables restricted to assume discrete values, which are linear and separable from the continuous variables. The strategy of releasing nonbasic variables from their bounds, combined with the “active constraint” method, has been developed. This strategy is used to force the appropriate non-integer basic variables to move to their neighbourhood integer points. Successful implementation of these algorithms was achieved on various test problems.

  10. Systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces

    Directory of Open Access Journals (Sweden)

    Cho Yeol

    2011-01-01

    Full Text Available Abstract In this paper, the existing theorems and methods for finding solutions of systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces are studied. To overcome the difficulties, due to the presence of a proper convex lower semi-continuous function, φ and a mapping g, which appeared in the considered problem, we have used some applications of the resolvent operator technique. We would like to point out that although many authors have proved results for finding solutions of the systems of nonlinear set-valued (mixed variational inequalities problems, it is clear that it cannot be directly applied to the problems that we have considered in this paper because of φ and g. 2000 AMS Subject Classification: 47H05; 47H09; 47J25; 65J15.

  11. Variational structure of inverse problems in wave propagation and vibration

    Energy Technology Data Exchange (ETDEWEB)

    Berryman, J.G.

    1995-03-01

    Practical algorithms for solving realistic inverse problems may often be viewed as problems in nonlinear programming with the data serving as constraints. Such problems are most easily analyzed when it is possible to segment the solution space into regions that are feasible (satisfying all the known constraints) and infeasible (violating some of the constraints). Then, if the feasible set is convex or at least compact, the solution to the problem will normally lie on the boundary of the feasible set. A nonlinear program may seek the solution by systematically exploring the boundary while satisfying progressively more constraints. Examples of inverse problems in wave propagation (traveltime tomography) and vibration (modal analysis) will be presented to illustrate how the variational structure of these problems may be used to create nonlinear programs using implicit variational constraints.

  12. New preconditioned conjugate gradient algorithms for nonlinear unconstrained optimization problems

    International Nuclear Information System (INIS)

    Al-Bayati, A.; Al-Asadi, N.

    1997-01-01

    This paper presents two new predilection conjugate gradient algorithms for nonlinear unconstrained optimization problems and examines their computational performance. Computational experience shows that the new proposed algorithms generally imp lone the efficiency of Nazareth's [13] preconditioned conjugate gradient algorithm. (authors). 16 refs., 1 tab

  13. Genetic Algorithm for Mixed Integer Nonlinear Bilevel Programming and Applications in Product Family Design

    Directory of Open Access Journals (Sweden)

    Chenlu Miao

    2016-01-01

    Full Text Available Many leader-follower relationships exist in product family design engineering problems. We use bilevel programming (BLP to reflect the leader-follower relationship and describe such problems. Product family design problems have unique characteristics; thus, mixed integer nonlinear BLP (MINLBLP, which has both continuous and discrete variables and multiple independent lower-level problems, is widely used in product family optimization. However, BLP is difficult in theory and is an NP-hard problem. Consequently, using traditional methods to solve such problems is difficult. Genetic algorithms (GAs have great value in solving BLP problems, and many studies have designed GAs to solve BLP problems; however, such GAs are typically designed for special cases that do not involve MINLBLP with one or multiple followers. Therefore, we propose a bilevel GA to solve these particular MINLBLP problems, which are widely used in product family problems. We give numerical examples to demonstrate the effectiveness of the proposed algorithm. In addition, a reducer family case study is examined to demonstrate practical applications of the proposed BLGA.

  14. Sensitivity theory for general non-linear algebraic equations with constraints

    International Nuclear Information System (INIS)

    Oblow, E.M.

    1977-04-01

    Sensitivity theory has been developed to a high state of sophistication for applications involving solutions of the linear Boltzmann equation or approximations to it. The success of this theory in the field of radiation transport has prompted study of possible extensions of the method to more general systems of non-linear equations. Initial work in the U.S. and in Europe on the reactor fuel cycle shows that the sensitivity methodology works equally well for those non-linear problems studied to date. The general non-linear theory for algebraic equations is summarized and applied to a class of problems whose solutions are characterized by constrained extrema. Such equations form the basis of much work on energy systems modelling and the econometrics of power production and distribution. It is valuable to have a sensitivity theory available for these problem areas since it is difficult to repeatedly solve complex non-linear equations to find out the effects of alternative input assumptions or the uncertainties associated with predictions of system behavior. The sensitivity theory for a linear system of algebraic equations with constraints which can be solved using linear programming techniques is discussed. The role of the constraints in simplifying the problem so that sensitivity methodology can be applied is highlighted. The general non-linear method is summarized and applied to a non-linear programming problem in particular. Conclusions are drawn in about the applicability of the method for practical problems

  15. Iterative Adaptive Dynamic Programming for Solving Unknown Nonlinear Zero-Sum Game Based on Online Data.

    Science.gov (United States)

    Zhu, Yuanheng; Zhao, Dongbin; Li, Xiangjun

    2017-03-01

    H ∞ control is a powerful method to solve the disturbance attenuation problems that occur in some control systems. The design of such controllers relies on solving the zero-sum game (ZSG). But in practical applications, the exact dynamics is mostly unknown. Identification of dynamics also produces errors that are detrimental to the control performance. To overcome this problem, an iterative adaptive dynamic programming algorithm is proposed in this paper to solve the continuous-time, unknown nonlinear ZSG with only online data. A model-free approach to the Hamilton-Jacobi-Isaacs equation is developed based on the policy iteration method. Control and disturbance policies and value are approximated by neural networks (NNs) under the critic-actor-disturber structure. The NN weights are solved by the least-squares method. According to the theoretical analysis, our algorithm is equivalent to a Gauss-Newton method solving an optimization problem, and it converges uniformly to the optimal solution. The online data can also be used repeatedly, which is highly efficient. Simulation results demonstrate its feasibility to solve the unknown nonlinear ZSG. When compared with other algorithms, it saves a significant amount of online measurement time.

  16. Bayesian nonlinear regression for large small problems

    KAUST Repository

    Chakraborty, Sounak; Ghosh, Malay; Mallick, Bani K.

    2012-01-01

    Statistical modeling and inference problems with sample sizes substantially smaller than the number of available covariates are challenging. This is known as large p small n problem. Furthermore, the problem is more complicated when we have multiple correlated responses. We develop multivariate nonlinear regression models in this setup for accurate prediction. In this paper, we introduce a full Bayesian support vector regression model with Vapnik's ε-insensitive loss function, based on reproducing kernel Hilbert spaces (RKHS) under the multivariate correlated response setup. This provides a full probabilistic description of support vector machine (SVM) rather than an algorithm for fitting purposes. We have also introduced a multivariate version of the relevance vector machine (RVM). Instead of the original treatment of the RVM relying on the use of type II maximum likelihood estimates of the hyper-parameters, we put a prior on the hyper-parameters and use Markov chain Monte Carlo technique for computation. We have also proposed an empirical Bayes method for our RVM and SVM. Our methods are illustrated with a prediction problem in the near-infrared (NIR) spectroscopy. A simulation study is also undertaken to check the prediction accuracy of our models. © 2012 Elsevier Inc.

  17. Bayesian nonlinear regression for large small problems

    KAUST Repository

    Chakraborty, Sounak

    2012-07-01

    Statistical modeling and inference problems with sample sizes substantially smaller than the number of available covariates are challenging. This is known as large p small n problem. Furthermore, the problem is more complicated when we have multiple correlated responses. We develop multivariate nonlinear regression models in this setup for accurate prediction. In this paper, we introduce a full Bayesian support vector regression model with Vapnik\\'s ε-insensitive loss function, based on reproducing kernel Hilbert spaces (RKHS) under the multivariate correlated response setup. This provides a full probabilistic description of support vector machine (SVM) rather than an algorithm for fitting purposes. We have also introduced a multivariate version of the relevance vector machine (RVM). Instead of the original treatment of the RVM relying on the use of type II maximum likelihood estimates of the hyper-parameters, we put a prior on the hyper-parameters and use Markov chain Monte Carlo technique for computation. We have also proposed an empirical Bayes method for our RVM and SVM. Our methods are illustrated with a prediction problem in the near-infrared (NIR) spectroscopy. A simulation study is also undertaken to check the prediction accuracy of our models. © 2012 Elsevier Inc.

  18. On a mixed problem for a coupled nonlinear system

    Directory of Open Access Journals (Sweden)

    Marcondes R. Clark

    1997-03-01

    Full Text Available In this article we prove the existence and uniqueness of solutions to the mixed problem associated with the nonlinear system $$ u_{tt}-M(int_Omega |abla u|^2dxDelta u+|u|^ ho u+heta =f $$ $$ heta _t -Delta heta +u_{t}=g $$ where $M$ is a positive real function, and $f$ and $g$ are known real functions.

  19. Green's function-stochastic methods framework for probing nonlinear evolution problems: Burger's equation, the nonlinear Schroedinger's equation, and hydrodynamic organization of near-molecular-scale vorticity

    International Nuclear Information System (INIS)

    Keanini, R.G.

    2011-01-01

    Research highlights: → Systematic approach for physically probing nonlinear and random evolution problems. → Evolution of vortex sheets corresponds to evolution of an Ornstein-Uhlenbeck process. → Organization of near-molecular scale vorticity mediated by hydrodynamic modes. → Framework allows calculation of vorticity evolution within random strain fields. - Abstract: A framework which combines Green's function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green's function and stochastic representative solutions of linear drift-diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems - Burgers' equation and the nonlinear Schroedinger's equation - are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole-Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger's vortex sheets. Here, the governing vorticity equation corresponds to the Fokker-Planck equation of an Ornstein-Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the

  20. Global gradient estimates for divergence-type elliptic problems involving general nonlinear operators

    Science.gov (United States)

    Cho, Yumi

    2018-05-01

    We study nonlinear elliptic problems with nonstandard growth and ellipticity related to an N-function. We establish global Calderón-Zygmund estimates of the weak solutions in the framework of Orlicz spaces over bounded non-smooth domains. Moreover, we prove a global regularity result for asymptotically regular problems which are getting close to the regular problems considered, when the gradient variable goes to infinity.

  1. Duality in non-linear programming

    Science.gov (United States)

    Jeyalakshmi, K.

    2018-04-01

    In this paper we consider duality and converse duality for a programming problem involving convex objective and constraint functions with finite dimensional range. We do not assume any constraint qualification. The dual is presented by reducing the problem to a standard Lagrange multiplier problem.

  2. Constrained non-linear optimization in 3D reflexion tomography; Problemes d'optimisation non-lineaire avec contraintes en tomographie de reflexion 3D

    Energy Technology Data Exchange (ETDEWEB)

    Delbos, F

    2004-11-01

    Reflexion tomography allows the determination of a subsurface velocity model from the travel times of seismic waves. The introduction of a priori information in this inverse problem can lead to the resolution of a constrained non-linear least-squares problem. The goal of the thesis is to improve the resolution techniques of this optimization problem, whose main difficulties are its ill-conditioning, its large scale and an expensive cost function in terms of CPU time. Thanks to a detailed study of the problem and to numerous numerical experiments, we justify the use of a sequential quadratic programming method, in which the tangential quadratic programs are solved by an original augmented Lagrangian method. We show the global linear convergence of the latter. The efficiency and robustness of the approach are demonstrated on several synthetic examples and on two real data cases. (author)

  3. Piecewise-linear and bilinear approaches to nonlinear differential equations approximation problem of computational structural mechanics

    OpenAIRE

    Leibov Roman

    2017-01-01

    This paper presents a bilinear approach to nonlinear differential equations system approximation problem. Sometimes the nonlinear differential equations right-hand sides linearization is extremely difficult or even impossible. Then piecewise-linear approximation of nonlinear differential equations can be used. The bilinear differential equations allow to improve piecewise-linear differential equations behavior and reduce errors on the border of different linear differential equations systems ...

  4. Quasi-stability of a vector trajectorial problem with non-linear partial criteria

    Directory of Open Access Journals (Sweden)

    Vladimir A. Emelichev

    2003-10-01

    Full Text Available Multi-objective (vector combinatorial problem of finding the Pareto set with four kinds of non-linear partial criteria is considered. Necessary and sufficient conditions of that kind of stability of the problem (quasi-stability are obtained. The problem is a discrete analogue of the lower semicontinuity by Hausdorff of the optimal mapping. Mathematics Subject Classification 2000: 90C10, 90C05, 90C29, 90C31.

  5. Use Residual Correction Method and Monotone Iterative Technique to Calculate the Upper and Lower Approximate Solutions of Singularly Perturbed Non-linear Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Chi-Chang Wang

    2013-09-01

    Full Text Available This paper seeks to use the proposed residual correction method in coordination with the monotone iterative technique to obtain upper and lower approximate solutions of singularly perturbed non-linear boundary value problems. First, the monotonicity of a non-linear differential equation is reinforced using the monotone iterative technique, then the cubic-spline method is applied to discretize and convert the differential equation into the mathematical programming problems of an inequation, and finally based on the residual correction concept, complex constraint solution problems are transformed into simpler questions of equational iteration. As verified by the four examples given in this paper, the method proposed hereof can be utilized to fast obtain the upper and lower solutions of questions of this kind, and to easily identify the error range between mean approximate solutions and exact solutions.

  6. JAC3D -- A three-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method; Yucca Mountain Site Characterization Project

    Energy Technology Data Exchange (ETDEWEB)

    Biffle, J.H.

    1993-02-01

    JAC3D is a three-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equation. The method is implemented in a three-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. An eight-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic-plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.

  7. JAC2D: A two-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method; Yucca Mountain Site Characterization Project

    Energy Technology Data Exchange (ETDEWEB)

    Biffle, J.H.; Blanford, M.L.

    1994-05-01

    JAC2D is a two-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equations. The method is implemented in a two-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. A four-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic/plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.

  8. MINPACK-1, Subroutine Library for Nonlinear Equation System

    International Nuclear Information System (INIS)

    Garbow, Burton S.

    1984-01-01

    1 - Description of problem or function: MINPACK1 is a package of FORTRAN subprograms for the numerical solution of systems of non- linear equations and nonlinear least-squares problems. The individual programs are: Identification/Description: - CHKDER: Check gradients for consistency with functions, - DOGLEG: Determine combination of Gauss-Newton and gradient directions, - DPMPAR: Provide double precision machine parameters, - ENORM: Calculate Euclidean norm of vector, - FDJAC1: Calculate difference approximation to Jacobian (nonlinear equations), - FDJAC2: Calculate difference approximation to Jacobian (least squares), - HYBRD: Solve system of nonlinear equations (approximate Jacobian), - HYBRD1: Easy-to-use driver for HYBRD, - HYBRJ: Solve system of nonlinear equations (analytic Jacobian), - HYBRJ1: Easy-to-use driver for HYBRJ, - LMDER: Solve nonlinear least squares problem (analytic Jacobian), - LMDER1: Easy-to-use driver for LMDER, - LMDIF: Solve nonlinear least squares problem (approximate Jacobian), - LMDIF1: Easy-to-use driver for LMDIF, - LMPAR: Determine Levenberg-Marquardt parameter - LMSTR: Solve nonlinear least squares problem (analytic Jacobian, storage conserving), - LMSTR1: Easy-to-use driver for LMSTR, - QFORM: Accumulate orthogonal matrix from QR factorization QRFAC Compute QR factorization of rectangular matrix, - QRSOLV: Complete solution of least squares problem, - RWUPDT: Update QR factorization after row addition, - R1MPYQ: Apply orthogonal transformations from QR factorization, - R1UPDT: Update QR factorization after rank-1 addition, - SPMPAR: Provide single precision machine parameters. 4. Method of solution - MINPACK1 uses the modified Powell hybrid method and the Levenberg-Marquardt algorithm

  9. Nonlinear Preconditioning and its Application in Multicomponent Problems

    KAUST Repository

    Liu, Lulu

    2015-12-07

    The Multiplicative Schwarz Preconditioned Inexact Newton (MSPIN) algorithm is presented as a complement to Additive Schwarz Preconditioned Inexact Newton (ASPIN). At an algebraic level, ASPIN and MSPIN are variants of the same strategy to improve the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partitioning of degrees of freedom in a nonlinear PDE system by field type rather than by subdomain, where a modest factor of concurrency can be sacrificed for physically motivated convergence robustness. ASPIN, originally introduced for decompositions into subdomains, is natural for high concurrency and reduction of global synchronization. The ASPIN framework, as an option for the outermost solver, successfully handles strong nonlinearities in computational fluid dynamics, but is barely explored for the highly nonlinear models of complex multiphase flow with capillarity, heterogeneity, and complex geometry. In this dissertation, the fully implicit ASPIN method is demonstrated for a finite volume discretization based on incompressible two-phase reservoir simulators in the presence of capillary forces and gravity. Numerical experiments show that the number of global nonlinear iterations is not only scalable with respect to the number of processors, but also significantly reduced compared with the standard inexact Newton method with a backtracking technique. Moreover, the ASPIN method, in contrast with the IMPES method, saves overall execution time because of the savings in timestep size. We consider the additive and multiplicative types of inexact Newton algorithms in the field-split context, and we augment the classical convergence theory of ASPIN for the multiplicative case. Moreover, we provide the convergence analysis of the MSPIN algorithm. Under suitable assumptions, it is shown that MSPIN is locally convergent, and desired superlinear or even quadratic convergence can be

  10. Fermat collocation method for the solutions of nonlinear system of second order boundary value problems

    Directory of Open Access Journals (Sweden)

    Salih Yalcinbas

    2016-01-01

    Full Text Available In this study, a numerical approach is proposed to obtain approximate solutions of nonlinear system of second order boundary value problem. This technique is essentially based on the truncated Fermat series and its matrix representations with collocation points. Using the matrix method, we reduce the problem system of nonlinear algebraic equations. Numerical examples are also given to demonstrate the validity and applicability of the presented technique. The method is easy to implement and produces accurate results.

  11. Domain decomposition based iterative methods for nonlinear elliptic finite element problems

    Energy Technology Data Exchange (ETDEWEB)

    Cai, X.C. [Univ. of Colorado, Boulder, CO (United States)

    1994-12-31

    The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.

  12. Numerical solution of non-linear diffusion problems

    International Nuclear Information System (INIS)

    Carmen, A. del; Ferreri, J.C.

    1998-01-01

    This paper presents a method for the numerical solution of non-linear diffusion problems using finite-differences in moving grids. Due to the presence of steep fronts in the solution domain and to the presence of advective terms originating in the grid movement, an implicit TVD scheme, first order in time and second order in space has been developed. Some algebraic details of the derivation are given. Results are shown for the pure advection of a scalar as a test case and an example dealing with the slow spreading of viscous fluids over plane surfaces. The agreement between numerical and analytical solutions is excellent. (author). 8 refs., 3 figs

  13. Iterative Runge–Kutta-type methods for nonlinear ill-posed problems

    International Nuclear Information System (INIS)

    Böckmann, C; Pornsawad, P

    2008-01-01

    We present a regularization method for solving nonlinear ill-posed problems by applying the family of Runge–Kutta methods to an initial value problem, in particular, to the asymptotical regularization method. We prove that the developed iterative regularization method converges to a solution under certain conditions and with a general stopping rule. Some particular iterative regularization methods are numerically implemented. Numerical results of the examples show that the developed Runge–Kutta-type regularization methods yield stable solutions and that particular implicit methods are very efficient in saving iteration steps

  14. Constrained non-linear optimization in 3D reflexion tomography; Problemes d'optimisation non-lineaire avec contraintes en tomographie de reflexion 3D

    Energy Technology Data Exchange (ETDEWEB)

    Delbos, F.

    2004-11-01

    Reflexion tomography allows the determination of a subsurface velocity model from the travel times of seismic waves. The introduction of a priori information in this inverse problem can lead to the resolution of a constrained non-linear least-squares problem. The goal of the thesis is to improve the resolution techniques of this optimization problem, whose main difficulties are its ill-conditioning, its large scale and an expensive cost function in terms of CPU time. Thanks to a detailed study of the problem and to numerous numerical experiments, we justify the use of a sequential quadratic programming method, in which the tangential quadratic programs are solved by an original augmented Lagrangian method. We show the global linear convergence of the latter. The efficiency and robustness of the approach are demonstrated on several synthetic examples and on two real data cases. (author)

  15. On the quantum inverse problem for a new type of nonlinear Schroedinger equation for Alfven waves in plasma

    International Nuclear Information System (INIS)

    Sen, S.; Roy Chowdhury, A.

    1989-06-01

    The nonlinear Alfven waves are governed by the Vector Derivative nonlinear Schroedinger (VDNLS) equation, which for parallel or quasi parallel propagation reduces to the Derivative Nonlinear Schroedinger (DNLS) equation for the circularly polarized waves. We have formulated the Quantum Inverse problem for a new type of Nonlinear Schroedinger Equation which has many properties similar to the usual NLS problem but the structure of classical and quantum R matrix are distinctly different. The commutation rules of the scattering data are obtained and the Algebraic Bethe Ansatz is formulated to derive the eigenvalue equation for the energy of the excited states. 10 refs

  16. An Algorithmic Comparison of the Hyper-Reduction and the Discrete Empirical Interpolation Method for a Nonlinear Thermal Problem

    Directory of Open Access Journals (Sweden)

    Felix Fritzen

    2018-02-01

    Full Text Available A novel algorithmic discussion of the methodological and numerical differences of competing parametric model reduction techniques for nonlinear problems is presented. First, the Galerkin reduced basis (RB formulation is presented, which fails at providing significant gains with respect to the computational efficiency for nonlinear problems. Renowned methods for the reduction of the computing time of nonlinear reduced order models are the Hyper-Reduction and the (Discrete Empirical Interpolation Method (EIM, DEIM. An algorithmic description and a methodological comparison of both methods are provided. The accuracy of the predictions of the hyper-reduced model and the (DEIM in comparison to the Galerkin RB is investigated. All three approaches are applied to a simple uncertainty quantification of a planar nonlinear thermal conduction problem. The results are compared to computationally intense finite element simulations.

  17. Polyharmonic boundary value problems positivity preserving and nonlinear higher order elliptic equations in bounded domains

    CERN Document Server

    Gazzola, Filippo; Sweers, Guido

    2010-01-01

    This monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. Underlying models and, in particular, the role of different boundary conditions are explained in detail. As for linear problems, after a brief summary of the existence theory and Lp and Schauder estimates, the focus is on positivity or - since, in contrast to second order equations, a general form of a comparison principle does not exist - on “near positivity.” The required kernel estimates are also presented in detail. As for nonlinear problems, several techniques well-known from second order equations cannot be utilized and have to be replaced by new and different methods. Subcritical, critical and supercritical nonlinearities are discussed and various existence and nonexistence results are proved. The interplay with the positivity topic from the first part is emphasized and, moreover, a far-reaching Gidas-Ni-Nirenbe...

  18. On the Cauchy problem for nonlinear Schrödinger equations with rotation

    KAUST Repository

    Antonelli, Paolo; Marahrens, Daniel; Sparber, Christof

    2011-01-01

    We consider the Cauchy problem for (energy-subcritical) nonlinear Schrödinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a well-known model for superuid quantum gases in rotating traps. We prove global existence (in the energy space) for defocusing nonlinearities without any restriction on the rotation frequency, generalizing earlier results given in [11, 12]. Moreover, we find that the rotation term has a considerable in fiuence in proving finite time blow-up in the focusing case.

  19. On the Cauchy problem for nonlinear Schrödinger equations with rotation

    KAUST Repository

    Antonelli, Paolo

    2011-10-01

    We consider the Cauchy problem for (energy-subcritical) nonlinear Schrödinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a well-known model for superuid quantum gases in rotating traps. We prove global existence (in the energy space) for defocusing nonlinearities without any restriction on the rotation frequency, generalizing earlier results given in [11, 12]. Moreover, we find that the rotation term has a considerable in fiuence in proving finite time blow-up in the focusing case.

  20. Existence of bounded solutions of Neumann problem for a nonlinear degenerate elliptic equation

    Directory of Open Access Journals (Sweden)

    Salvatore Bonafede

    2017-10-01

    Full Text Available We prove the existence of bounded solutions of Neumann problem for nonlinear degenerate elliptic equations of second order in divergence form. We also study some properties as the Phragmen-Lindelof property and the asymptotic behavior of the solutions of Dirichlet problem associated to our equation in an unbounded domain.

  1. Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media

    KAUST Repository

    Yang, Haijian

    2016-07-26

    Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.

  2. Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media

    KAUST Repository

    Yang, Haijian; Yang, Chao; Sun, Shuyu

    2016-01-01

    Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.

  3. Spectral methods for a nonlinear initial value problem involving pseudo differential operators

    International Nuclear Information System (INIS)

    Pasciak, J.E.

    1982-01-01

    Spectral methods (Fourier methods) for approximating the solution of a nonlinear initial value problem involving pseudo differential operators are defined and analyzed. A semidiscrete approximation to the nonlinear equation based on an L 2 projection is described. The semidiscrete L 2 approximation is shown to be a priori stable and convergent under sufficient decay and smoothness assumptions on the initial data. It is shown that the semidiscrete method converges with infinite order, that is, higher order decay and smoothness assumptions imply higher order error bounds. Spectral schemes based on spacial collocation are also discussed

  4. Initial-value problem for the Gardner equation applied to nonlinear internal waves

    Science.gov (United States)

    Rouvinskaya, Ekaterina; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim

    2017-04-01

    The Gardner equation is a fundamental mathematical model for the description of weakly nonlinear weakly dispersive internal waves, when cubic nonlinearity cannot be neglected. Within this model coefficients of quadratic and cubic nonlinearity can both be positive as well as negative, depending on background conditions of the medium, where waves propagate (sea water density stratification, shear flow profile) [Rouvinskaya et al., 2014, Kurkina et al., 2011, 2015]. For the investigation of weakly dispersive behavior in the framework of nondimensional Gardner equation with fixed (positive) sign of quadratic nonlinearity and positive or negative cubic nonlinearity {eq1} partial η/partial t+6η( {1± η} )partial η/partial x+partial ^3η/partial x^3=0, } the series of numerical experiments of initial-value problem was carried out for evolution of a bell-shaped impulse of negative polarity (opposite to the sign of quadratic nonlinear coefficient): {eq2} η(x,t=0)=-asech2 ( {x/x0 } ), for which amplitude a and width x0 was varied. Similar initial-value problem was considered in the paper [Trillo et al., 2016] for the Korteweg - de Vries equation. For the Gardner equation with different signs of cubic nonlinearity the initial-value problem for piece-wise constant initial condition was considered in detail in [Grimshaw et al., 2002, 2010]. It is widely known, for example, [Pelinovsky et al., 2007], that the Gardner equation (1) with negative cubic nonlinearity has a family of classic solitary wave solutions with only positive polarity,and with limiting amplitude equal to 1. Therefore evolution of impulses (2) of negative polarity (whose amplitudes a were varied from 0.1 to 3, and widths at the level of a/2 were equal to triple width of solitons with the same amplitude for a 1) was going on a universal scenario with the generation of nonlinear Airy wave. For the Gardner equation (1) with the positive cubic nonlinearity coefficient there exist two one-parametric families of

  5. Invert 1.0: A program for solving the nonlinear inverse heat conduction problem for one-dimensional solids

    International Nuclear Information System (INIS)

    Snider, D.M.

    1981-02-01

    INVERT 1.0 is a digital computer program written in FORTRAN IV which calculates the surface heat flux of a one-dimensional solid using an interior-measured temperature and a physical description of the solid. By using two interior-measured temperatures, INVERT 1.0 can provide a solution for the heat flux at two surfaces, the heat flux at a boundary and the time dependent power, or the heat flux at a boundary and the time varying thermal conductivity of a material composing the solid. The analytical solution to inversion problem is described for the one-dimensional cylinder, sphere, or rectangular slab. The program structure, input instructions, and sample problems demonstrating the accuracy of the solution technique are included

  6. A Simple FEM Formulation Applied to Nonlinear Problems of Impact with Thermomechanical Coupling

    Directory of Open Access Journals (Sweden)

    João Paulo de Barros Cavalcante

    Full Text Available Abstract The thermal effects of problems involving deformable structures are essential to describe the behavior of materials in feasible terms. Verifying the transformation of mechanical energy into heat it is possible to predict the modifications of mechanical properties of materials due to its temperature changes. The current paper presents the numerical development of a finite element method suitable for nonlinear structures coupled with thermomechanical behavior; including impact problems. A simple and effective alternative formulation is presented, called FEM positional, to deal with the dynamic nonlinear systems. The developed numerical is based on the minimum potential energy written in terms of nodal positions instead of displacements. The effects of geometrical, material and thermal nonlinearities are considered. The thermodynamically consistent formulation is based on the laws of thermodynamics and the Helmholtz free-energy, used to describe the thermoelastic and the thermoplastic behaviors. The coupled thermomechanical model can result in secondary effects that cause redistributions of internal efforts, depending on the history of deformation and material properties. The numerical results of the proposed formulation are compared with examples found in the literature.

  7. Adaptive discretizations for the choice of a Tikhonov regularization parameter in nonlinear inverse problems

    International Nuclear Information System (INIS)

    Kaltenbacher, Barbara; Kirchner, Alana; Vexler, Boris

    2011-01-01

    Parameter identification problems for partial differential equations usually lead to nonlinear inverse problems. A typical property of such problems is their instability, which requires regularization techniques, like, e.g., Tikhonov regularization. The main focus of this paper will be on efficient methods for determining a suitable regularization parameter by using adaptive finite element discretizations based on goal-oriented error estimators. A well-established method for the determination of a regularization parameter is the discrepancy principle where the residual norm, considered as a function i of the regularization parameter, should equal an appropriate multiple of the noise level. We suggest to solve the resulting scalar nonlinear equation by an inexact Newton method, where in each iteration step, a regularized problem is solved at a different discretization level. The proposed algorithm is an extension of the method suggested in Griesbaum A et al (2008 Inverse Problems 24 025025) for linear inverse problems, where goal-oriented error estimators for i and its derivative are used for adaptive refinement strategies in order to keep the discretization level as coarse as possible to save computational effort but fine enough to guarantee global convergence of the inexact Newton method. This concept leads to a highly efficient method for determining the Tikhonov regularization parameter for nonlinear ill-posed problems. Moreover, we prove that with the so-obtained regularization parameter and an also adaptively discretized Tikhonov minimizer, usual convergence and regularization results from the continuous setting can be recovered. As a matter of fact, it is shown that it suffices to use stationary points of the Tikhonov functional. The efficiency of the proposed method is demonstrated by means of numerical experiments. (paper)

  8. Stokes phenomena and monodromy deformation problem for nonlinear Schrodinger equation

    International Nuclear Information System (INIS)

    Chowdury, A.R.; Naskar, M.

    1986-01-01

    Following Flaschka and Newell, the inverse problem for Painleve IV is formulated with the help of similarity variables. The Painleve IV arises as the eliminant of the two second-order ordinary differential equations originating from the nonlinear Schrodinger equation. Asymptotic expansions are obtained near the singularities at zero and infinity of the complex eigenvalue plane. The corresponding analysis then displays the Stokes phenomena. The monodromy matrices connecting the solution Y /sub j/ in the sector S /sub j/ to that in S /sub j+1/ are fixed in structure by the imposition of certain conditions. It is then shown that a deformation keeping the monodromy data fixed leads to the nonlinear Schrodinger equation. While Flaschka and Newell did not make any absolute determination of the Stokes parameters, the present approach yields the values of the Stokes parameters in an explicit way, which in turn can determine the matrix connecting the solutions near zero and infinity. Finally, it is shown that the integral equation originating from the analyticity and asymptotic nature of the problem leads to the similarity solution previously determined by Boiti and Pampinelli

  9. A nonlinear complementarity approach for the national energy modeling system

    International Nuclear Information System (INIS)

    Gabriel, S.A.; Kydes, A.S.

    1995-01-01

    The National Energy Modeling System (NEMS) is a large-scale mathematical model that computes equilibrium fuel prices and quantities in the U.S. energy sector. At present, to generate these equilibrium values, NEMS sequentially solves a collection of linear programs and nonlinear equations. The NEMS solution procedure then incorporates the solutions of these linear programs and nonlinear equations in a nonlinear Gauss-Seidel approach. The authors describe how the current version of NEMS can be formulated as a particular nonlinear complementarity problem (NCP), thereby possibly avoiding current convergence problems. In addition, they show that the NCP format is equally valid for a more general form of NEMS. They also describe several promising approaches for solving the NCP form of NEMS based on recent Newton type methods for general NCPs. These approaches share the feature of needing to solve their direction-finding subproblems only approximately. Hence, they can effectively exploit the sparsity inherent in the NEMS NCP

  10. Parallel Nonlinear Optimization for Astrodynamic Navigation, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — CU Aerospace proposes the development of a new parallel nonlinear program (NLP) solver software package. NLPs allow the solution of complex optimization problems,...

  11. A solution procedure for mixed-integer nonlinear programming formulation of supply chain planning with quantity discounts under demand uncertainty

    Science.gov (United States)

    Yin, Sisi; Nishi, Tatsushi

    2014-11-01

    Quantity discount policy is decision-making for trade-off prices between suppliers and manufacturers while production is changeable due to demand fluctuations in a real market. In this paper, quantity discount models which consider selection of contract suppliers, production quantity and inventory simultaneously are addressed. The supply chain planning problem with quantity discounts under demand uncertainty is formulated as a mixed-integer nonlinear programming problem (MINLP) with integral terms. We apply an outer-approximation method to solve MINLP problems. In order to improve the efficiency of the proposed method, the problem is reformulated as a stochastic model replacing the integral terms by using a normalisation technique. We present numerical examples to demonstrate the efficiency of the proposed method.

  12. Solving applied mathematical problems with Matlab

    CERN Document Server

    Xue, Dingyu

    2008-01-01

    Computer Mathematics Language-An Overview. Fundamentals of MATLAB Programming. Calculus Problems. MATLAB Computations of Linear Algebra Problems. Integral Transforms and Complex Variable Functions. Solutions to Nonlinear Equations and Optimization Problems. MATLAB Solutions to Differential Equation Problems. Solving Interpolations and Approximations Problems. Solving Probability and Mathematical Statistics Problems. Nontraditional Solution Methods for Mathematical Problems.

  13. Interior Point Methods for Large-Scale Nonlinear Programming

    Czech Academy of Sciences Publication Activity Database

    Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan

    2005-01-01

    Roč. 20, č. 4-5 (2005), s. 569-582 ISSN 1055-6788 R&D Projects: GA AV ČR IAA1030405 Institutional research plan: CEZ:AV0Z10300504 Keywords : nonlinear programming * interior point methods * KKT systems * indefinite preconditioners * filter methods * algorithms Subject RIV: BA - General Mathematics Impact factor: 0.477, year: 2005

  14. Numerical methods for the design of large-scale nonlinear discrete ill-posed inverse problems

    International Nuclear Information System (INIS)

    Haber, E; Horesh, L; Tenorio, L

    2010-01-01

    Design of experiments for discrete ill-posed problems is a relatively new area of research. While there has been some limited work concerning the linear case, little has been done to study design criteria and numerical methods for ill-posed nonlinear problems. We present an algorithmic framework for nonlinear experimental design with an efficient numerical implementation. The data are modeled as indirect, noisy observations of the model collected via a set of plausible experiments. An inversion estimate based on these data is obtained by a weighted Tikhonov regularization whose weights control the contribution of the different experiments to the data misfit term. These weights are selected by minimization of an empirical estimate of the Bayes risk that is penalized to promote sparsity. This formulation entails a bilevel optimization problem that is solved using a simple descent method. We demonstrate the viability of our design with a problem in electromagnetic imaging based on direct current resistivity and magnetotelluric data

  15. Nonlinear model predictive control of a wave energy converter based on differential flatness parameterisation

    Science.gov (United States)

    Li, Guang

    2017-01-01

    This paper presents a fast constrained optimization approach, which is tailored for nonlinear model predictive control of wave energy converters (WEC). The advantage of this approach relies on its exploitation of the differential flatness of the WEC model. This can reduce the dimension of the resulting nonlinear programming problem (NLP) derived from the continuous constrained optimal control of WEC using pseudospectral method. The alleviation of computational burden using this approach helps to promote an economic implementation of nonlinear model predictive control strategy for WEC control problems. The method is applicable to nonlinear WEC models, nonconvex objective functions and nonlinear constraints, which are commonly encountered in WEC control problems. Numerical simulations demonstrate the efficacy of this approach.

  16. Mixed integer nonlinear programming model of wireless pricing scheme with QoS attribute of bandwidth and end-to-end delay

    Science.gov (United States)

    Irmeilyana, Puspita, Fitri Maya; Indrawati

    2016-02-01

    The pricing for wireless networks is developed by considering linearity factors, elasticity price and price factors. Mixed Integer Nonlinear Programming of wireless pricing model is proposed as the nonlinear programming problem that can be solved optimally using LINGO 13.0. The solutions are expected to give some information about the connections between the acceptance factor and the price. Previous model worked on the model that focuses on bandwidth as the QoS attribute. The models attempt to maximize the total price for a connection based on QoS parameter. The QoS attributes used will be the bandwidth and the end to end delay that affect the traffic. The maximum goal to maximum price is achieved when the provider determine the requirement for the increment or decrement of price change due to QoS change and amount of QoS value.

  17. Optimization for nonlinear inverse problem

    International Nuclear Information System (INIS)

    Boyadzhiev, G.; Brandmayr, E.; Pinat, T.; Panza, G.F.

    2007-06-01

    The nonlinear inversion of geophysical data in general does not yield a unique solution, but a single model, representing the investigated field, is preferred for an easy geological interpretation of the observations. The analyzed region is constituted by a number of sub-regions where the multi-valued nonlinear inversion is applied, which leads to a multi-valued solution. Therefore, combining the values of the solution in each sub-region, many acceptable models are obtained for the entire region and this complicates the geological interpretation of geophysical investigations. In this paper are presented new methodologies, capable to select one model, among all acceptable ones, that satisfies different criteria of smoothness in the explored space of solutions. In this work we focus on the non-linear inversion of surface waves dispersion curves, which gives structural models of shear-wave velocity versus depth, but the basic concepts have a general validity. (author)

  18. Multi-objective genetic algorithm for solving N-version program design problem

    Energy Technology Data Exchange (ETDEWEB)

    Yamachi, Hidemi [Department of Computer and Information Engineering, Nippon Institute of Technology, Miyashiro, Saitama 345-8501 (Japan) and Department of Production and Information Systems Engineering, Tokyo Metropolitan Institute of Technology, Hino, Tokyo 191-0065 (Japan)]. E-mail: yamachi@nit.ac.jp; Tsujimura, Yasuhiro [Department of Computer and Information Engineering, Nippon Institute of Technology, Miyashiro, Saitama 345-8501 (Japan)]. E-mail: tujimr@nit.ac.jp; Kambayashi, Yasushi [Department of Computer and Information Engineering, Nippon Institute of Technology, Miyashiro, Saitama 345-8501 (Japan)]. E-mail: yasushi@nit.ac.jp; Yamamoto, Hisashi [Department of Production and Information Systems Engineering, Tokyo Metropolitan Institute of Technology, Hino, Tokyo 191-0065 (Japan)]. E-mail: yamamoto@cc.tmit.ac.jp

    2006-09-15

    N-version programming (NVP) is a programming approach for constructing fault tolerant software systems. Generally, an optimization model utilized in NVP selects the optimal set of versions for each module to maximize the system reliability and to constrain the total cost to remain within a given budget. In such a model, while the number of versions included in the obtained solution is generally reduced, the budget restriction may be so rigid that it may fail to find the optimal solution. In order to ameliorate this problem, this paper proposes a novel bi-objective optimization model that maximizes the system reliability and minimizes the system total cost for designing N-version software systems. When solving multi-objective optimization problem, it is crucial to find Pareto solutions. It is, however, not easy to obtain them. In this paper, we propose a novel bi-objective optimization model that obtains many Pareto solutions efficiently. We formulate the optimal design problem of NVP as a bi-objective 0-1 nonlinear integer programming problem. In order to overcome this problem, we propose a Multi-objective genetic algorithm (MOGA), which is a powerful, though time-consuming, method to solve multi-objective optimization problems. When implementing genetic algorithm (GA), the use of an appropriate genetic representation scheme is one of the most important issues to obtain good performance. We employ random-key representation in our MOGA to find many Pareto solutions spaced as evenly as possible along the Pareto frontier. To pursue improve further performance, we introduce elitism, the Pareto-insertion and the Pareto-deletion operations based on distance between Pareto solutions in the selection process. The proposed MOGA obtains many Pareto solutions along the Pareto frontier evenly. The user of the MOGA can select the best compromise solution among the candidates by controlling the balance between the system reliability and the total cost.

  19. Multi-objective genetic algorithm for solving N-version program design problem

    International Nuclear Information System (INIS)

    Yamachi, Hidemi; Tsujimura, Yasuhiro; Kambayashi, Yasushi; Yamamoto, Hisashi

    2006-01-01

    N-version programming (NVP) is a programming approach for constructing fault tolerant software systems. Generally, an optimization model utilized in NVP selects the optimal set of versions for each module to maximize the system reliability and to constrain the total cost to remain within a given budget. In such a model, while the number of versions included in the obtained solution is generally reduced, the budget restriction may be so rigid that it may fail to find the optimal solution. In order to ameliorate this problem, this paper proposes a novel bi-objective optimization model that maximizes the system reliability and minimizes the system total cost for designing N-version software systems. When solving multi-objective optimization problem, it is crucial to find Pareto solutions. It is, however, not easy to obtain them. In this paper, we propose a novel bi-objective optimization model that obtains many Pareto solutions efficiently. We formulate the optimal design problem of NVP as a bi-objective 0-1 nonlinear integer programming problem. In order to overcome this problem, we propose a Multi-objective genetic algorithm (MOGA), which is a powerful, though time-consuming, method to solve multi-objective optimization problems. When implementing genetic algorithm (GA), the use of an appropriate genetic representation scheme is one of the most important issues to obtain good performance. We employ random-key representation in our MOGA to find many Pareto solutions spaced as evenly as possible along the Pareto frontier. To pursue improve further performance, we introduce elitism, the Pareto-insertion and the Pareto-deletion operations based on distance between Pareto solutions in the selection process. The proposed MOGA obtains many Pareto solutions along the Pareto frontier evenly. The user of the MOGA can select the best compromise solution among the candidates by controlling the balance between the system reliability and the total cost

  20. An Improved Dynamic Programming Decomposition Approach for Network Revenue Management

    OpenAIRE

    Dan Zhang

    2011-01-01

    We consider a nonlinear nonseparable functional approximation to the value function of a dynamic programming formulation for the network revenue management (RM) problem with customer choice. We propose a simultaneous dynamic programming approach to solve the resulting problem, which is a nonlinear optimization problem with nonlinear constraints. We show that our approximation leads to a tighter upper bound on optimal expected revenue than some known bounds in the literature. Our approach can ...

  1. Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's

    Science.gov (United States)

    Cai, Wei; Wang, Jian-Zhong

    1993-01-01

    We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.

  2. Numeric treatment of nonlinear second order multi-point boundary value problems using ANN, GAs and sequential quadratic programming technique

    Directory of Open Access Journals (Sweden)

    Zulqurnain Sabir

    2014-06-01

    Full Text Available In this paper, computational intelligence technique are presented for solving multi-point nonlinear boundary value problems based on artificial neural networks, evolutionary computing approach, and active-set technique. The neural network is to provide convenient methods for obtaining useful model based on unsupervised error for the differential equations. The motivation for presenting this work comes actually from the aim of introducing a reliable framework that combines the powerful features of ANN optimized with soft computing frameworks to cope with such challenging system. The applicability and reliability of such methods have been monitored thoroughly for various boundary value problems arises in science, engineering and biotechnology as well. Comprehensive numerical experimentations have been performed to validate the accuracy, convergence, and robustness of the designed scheme. Comparative studies have also been made with available standard solution to analyze the correctness of the proposed scheme.

  3. Continuous nonlinear optimization for engineering applications in GAMS technology

    CERN Document Server

    Andrei, Neculai

    2017-01-01

    This book presents the theoretical details and computational performances of algorithms used for solving continuous nonlinear optimization applications imbedded in GAMS. Aimed toward scientists and graduate students who utilize optimization methods to model and solve problems in mathematical programming, operations research, business, engineering, and industry, this book enables readers with a background in nonlinear optimization and linear algebra to use GAMS technology to understand and utilize its important capabilities to optimize algorithms for modeling and solving complex, large-scale, continuous nonlinear optimization problems or applications. Beginning with an overview of constrained nonlinear optimization methods, this book moves on to illustrate key aspects of mathematical modeling through modeling technologies based on algebraically oriented modeling languages. Next, the main feature of GAMS, an algebraically oriented language that allows for high-level algebraic representation of mathematical opti...

  4. Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities

    Indian Academy of Sciences (India)

    In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all R R . Assuming the existence of an upper and of a lower ...

  5. A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems

    Directory of Open Access Journals (Sweden)

    S. S. Motsa

    2013-01-01

    Full Text Available We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM, is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.

  6. Stochastic control theory dynamic programming principle

    CERN Document Server

    Nisio, Makiko

    2015-01-01

    This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems. First we consider completely observable control problems with finite horizons. Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton–Jacobi–Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory. When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise. This problem is treated in the same frameworks, via the nonlinear semigroup. Its results are applicable to the American option price problem. Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-ma...

  7. Three-Field Modelling of Nonlinear Nonsmooth Boundary Value Problems and Stability of Differential Mixed Variational Inequalities

    Directory of Open Access Journals (Sweden)

    J. Gwinner

    2013-01-01

    Full Text Available The purpose of this paper is twofold. Firstly we consider nonlinear nonsmooth elliptic boundary value problems, and also related parabolic initial boundary value problems that model in a simplified way steady-state unilateral contact with Tresca friction in solid mechanics, respectively, stem from nonlinear transient heat conduction with unilateral boundary conditions. Here a recent duality approach, that augments the classical Babuška-Brezzi saddle point formulation for mixed variational problems to twofold saddle point formulations, is extended to the nonsmooth problems under consideration. This approach leads to variational inequalities of mixed form for three coupled fields as unknowns and to related differential mixed variational inequalities in the time-dependent case. Secondly we are concerned with the stability of the solution set of a general class of differential mixed variational inequalities. Here we present a novel upper set convergence result with respect to perturbations in the data, including perturbations of the associated nonlinear maps, the nonsmooth convex functionals, and the convex constraint set. We employ epiconvergence for the convergence of the functionals and Mosco convergence for set convergence. We impose weak convergence assumptions on the perturbed maps using the monotonicity method of Browder and Minty.

  8. Menu-Driven Solver Of Linear-Programming Problems

    Science.gov (United States)

    Viterna, L. A.; Ferencz, D.

    1992-01-01

    Program assists inexperienced user in formulating linear-programming problems. A Linear Program Solver (ALPS) computer program is full-featured LP analysis program. Solves plain linear-programming problems as well as more-complicated mixed-integer and pure-integer programs. Also contains efficient technique for solution of purely binary linear-programming problems. Written entirely in IBM's APL2/PC software, Version 1.01. Packed program contains licensed material, property of IBM (copyright 1988, all rights reserved).

  9. Symbolic computation of analytic approximate solutions for nonlinear fractional differential equations

    Science.gov (United States)

    Lin, Yezhi; Liu, Yinping; Li, Zhibin

    2013-01-01

    The Adomian decomposition method (ADM) is one of the most effective methods to construct analytic approximate solutions for nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, Rach (2008) [22], the Adomian decomposition method and the Padé approximants technique, a new algorithm is proposed to construct analytic approximate solutions for nonlinear fractional differential equations with initial or boundary conditions. Furthermore, a MAPLE software package is developed to implement this new algorithm, which is user-friendly and efficient. One only needs to input the system equation, initial or boundary conditions and several necessary parameters, then our package will automatically deliver the analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the scope and demonstrate the validity of our package, especially for non-smooth initial value problems. Our package provides a helpful and easy-to-use tool in science and engineering simulations. Program summaryProgram title: ADMP Catalogue identifier: AENE_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENE_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 12011 No. of bytes in distributed program, including test data, etc.: 575551 Distribution format: tar.gz Programming language: MAPLE R15. Computer: PCs. Operating system: Windows XP/7. RAM: 2 Gbytes Classification: 4.3. Nature of problem: Constructing analytic approximate solutions of nonlinear fractional differential equations with initial or boundary conditions. Non-smooth initial value problems can be solved by this program. Solution method: Based on the new definition of the Adomian polynomials [1], the Adomian decomposition method and the Pad

  10. Special function solutions of a spectral problem for a nonlinear quantum oscillator

    International Nuclear Information System (INIS)

    Schulze-Halberg, A; Morris, J R

    2012-01-01

    We construct exact solutions of a spectral problem involving the Schrödinger equation for a nonlinear, one-parameter oscillator potential. In contrast to a previous analysis of the problem (Carinena et al 2007 Ann. Phys. 322 434–59), where solutions were given through a Rodrigues-type formula, our approach leads to closed-form representations of the solutions in terms of special functions, not containing any derivative operators. We show normalizability and orthogonality of our solutions, as well as correct reduction of the problem to the harmonic oscillator model, if the parameter in the potential gets close to zero. (paper)

  11. Multi-level nonlinear diffusion acceleration method for multigroup transport k-Eigenvalue problems

    International Nuclear Information System (INIS)

    Anistratov, Dmitriy Y.

    2011-01-01

    The nonlinear diffusion acceleration (NDA) method is an efficient and flexible transport iterative scheme for solving reactor-physics problems. This paper presents a fast iterative algorithm for solving multigroup neutron transport eigenvalue problems in 1D slab geometry. The proposed method is defined by a multi-level system of equations that includes multigroup and effective one-group low-order NDA equations. The Eigenvalue is evaluated in the exact projected solution space of smallest dimensionality, namely, by solving the effective one- group eigenvalue transport problem. Numerical results that illustrate performance of the new algorithm are demonstrated. (author)

  12. Lamé Parameter Estimation from Static Displacement Field Measurements in the Framework of Nonlinear Inverse Problems

    DEFF Research Database (Denmark)

    Hubmer, Simon; Sherina, Ekaterina; Neubauer, Andreas

    2018-01-01

    . The main result of this paper is the verification of a nonlinearity condition in an infinite dimensional Hilbert space context. This condition guarantees convergence of iterative regularization methods. Furthermore, numerical examples for recovery of the Lam´e parameters from displacement data simulating......We consider a problem of quantitative static elastography, the estimation of the Lam´e parameters from internal displacement field data. This problem is formulated as a nonlinear operator equation. To solve this equation, we investigate the Landweber iteration both analytically and numerically...... a static elastography experiment are presented....

  13. Nonlinear effects in dynamic analysis and design of nuclear power plant components: research status and needs

    Energy Technology Data Exchange (ETDEWEB)

    Stoykovich, M [Burns and Roe, Inc., New York (USA)

    1978-10-01

    This paper encompasses nonlinear effects in dynamic analysis and design of nuclear power plant facilities. The history of plasticity as a science is briefly discussed, and nonlinear cases of special interest are described. Approaches to some of the nonlinear problems are presented. These include the nonlinearity due to foundation-structure interaction associated with the base slab uplift during seismic disturbances, the nonlinear base-isolation system for the reduction of earthquake-generated forces and deformations of superstructures, nonlinear systems having restoring-force functions in case of gaps and liift-off conditions, and nonlinearity of viscoelastic systems due to inelastic deformations. Available computer programs information for the solution of various types of nonlinear problems are provided. Advantages and disadvantages of some of the nonlinear and linear analyses are discussed. Comparison of some nonlinear and linear results of analyses are presented. Conclusions are reached with regard to research status and recommendations for further studies and for performing non-linear analyses associated with the problems of nonlinearity are presented.

  14. Nonlinear effects in dynamic analysis and design of nuclear power plant components: research status and needs

    International Nuclear Information System (INIS)

    Stoykovich, M.

    1978-01-01

    This paper encompasses nonlinear effects in dynamic analysis and design of nuclear power plant facilities. The history of plasticity as a science is briefly discussed, and nonlinear cases of special interest are described. Approaches to some of the nonlinear problems are presented. These include the nonlinearity due to foundation-structure interaction associated with the base slab uplift during seismic disturbances, the nonlinear base-isolation system for the reduction of earthquake-generated forces and deformations of superstructures, nonlinear systems having restoring-force functions in case of gaps and liift-off conditions, and nonlinearity of viscoelastic systems due to inelastic deformations. Available computer programs information for the solution of various types of nonlinear problems are provided. Advantages and disadvantages of some of the nonlinear and linear analyses are discussed. Comparison of some nonlinear and linear results of analyses are presented. Conclusions are reached with regard to research status and recommendations for further studies and for performing non-linear analyses associated with the problems of nonlinearity are presented. (Auth.)

  15. A MODIFIED DECOMPOSITION METHOD FOR SOLVING NONLINEAR PROBLEM OF FLOW IN CONVERGING- DIVERGING CHANNEL

    Directory of Open Access Journals (Sweden)

    MOHAMED KEZZAR

    2015-08-01

    Full Text Available In this research, an efficient technique of computation considered as a modified decomposition method was proposed and then successfully applied for solving the nonlinear problem of the two dimensional flow of an incompressible viscous fluid between nonparallel plane walls. In fact this method gives the nonlinear term Nu and the solution of the studied problem as a power series. The proposed iterative procedure gives on the one hand a computationally efficient formulation with an acceleration of convergence rate and on the other hand finds the solution without any discretization, linearization or restrictive assumptions. The comparison of our results with those of numerical treatment and other earlier works shows clearly the higher accuracy and efficiency of the used Modified Decomposition Method.

  16. Strongly nonlinear nonhomogeneous elliptic unilateral problems with L^1 data and no sign conditions

    Directory of Open Access Journals (Sweden)

    Elhoussine Azroul

    2012-05-01

    Full Text Available In this article, we prove the existence of solutions to unilateral problems involving nonlinear operators of the form: $$ Au+H(x,u,abla u=f $$ where $A$ is a Leray Lions operator from $W_0^{1,p(x}(Omega$ into its dual $W^{-1,p'(x}(Omega$ and $H(x,s,xi$ is the nonlinear term satisfying some growth condition but no sign condition. The right hand side $f$ belong to $L^1(Omega$.

  17. On the solutions of the dKP equation: the nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking

    International Nuclear Information System (INIS)

    Manakov, S V; Santini, P M

    2008-01-01

    We have recently solved the inverse scattering problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev-Petviashvili (dKP) equation. We showed, in particular, that the associated inverse problems can be expressed in terms of nonlinear Riemann-Hilbert problems on the real axis. In this paper, we make use of the nonlinear Riemann-Hilbert problem of dKP (i) to construct the longtime behaviour of the solutions of its Cauchy problem; (ii) to characterize a class of implicit solutions; (iii) to elucidate the spectral mechanism causing the gradient catastrophe of localized solutions of dKP, at finite time as well as in the longtime regime, and the corresponding universal behaviours near breaking

  18. On the solutions of the dKP equation: the nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking

    Energy Technology Data Exchange (ETDEWEB)

    Manakov, S V [Landau Institute for Theoretical Physics, Moscow (Russian Federation); Santini, P M [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , and Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, Piazz.le Aldo Moro 2, I-00185 Rome (Italy)

    2008-02-08

    We have recently solved the inverse scattering problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev-Petviashvili (dKP) equation. We showed, in particular, that the associated inverse problems can be expressed in terms of nonlinear Riemann-Hilbert problems on the real axis. In this paper, we make use of the nonlinear Riemann-Hilbert problem of dKP (i) to construct the longtime behaviour of the solutions of its Cauchy problem; (ii) to characterize a class of implicit solutions; (iii) to elucidate the spectral mechanism causing the gradient catastrophe of localized solutions of dKP, at finite time as well as in the longtime regime, and the corresponding universal behaviours near breaking.

  19. Finite element solution of nonlinear eddy current problems with periodic excitation and its industrial applications.

    Science.gov (United States)

    Bíró, Oszkár; Koczka, Gergely; Preis, Kurt

    2014-05-01

    An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.

  20. A mixed-integer nonlinear programming approach to the optimal design of heat network in a polygeneration energy system

    International Nuclear Information System (INIS)

    Zhang, Jianyun; Liu, Pei; Zhou, Zhe; Ma, Linwei; Li, Zheng; Ni, Weidou

    2014-01-01

    Highlights: • Integration of heat streams with HRSG in a polygeneration system is studied. • A mixed-integer nonlinear programming model is proposed to optimize heat network. • Operating parameters and heat network configuration are optimized simultaneously. • The optimized heat network highly depends on the HRSG type and model specification. - Abstract: A large number of heat flows at various temperature and pressure levels exist in a polygeneration plant which co-produces electricity and chemical products. Integration of these external heat flows in a heat recovery steam generator (HRSG) has great potential to further enhance energy efficiency of such a plant; however, it is a challenging problem arising from the large design space of heat exchanger network. In this paper, a mixed-integer nonlinear programming model is developed for the design optimization of a HRSG with consideration of all alternative matches between the HRSG and external heat flows. This model is applied to four polygeneration cases with different HRSG types, and results indicate that the optimized heat network mainly depends on the HRSG type and the model specification

  1. State and parameter estimation in nonlinear systems as an optimal tracking problem

    International Nuclear Information System (INIS)

    Creveling, Daniel R.; Gill, Philip E.; Abarbanel, Henry D.I.

    2008-01-01

    In verifying and validating models of nonlinear processes it is important to incorporate information from observations in an efficient manner. Using the idea of synchronization of nonlinear dynamical systems, we present a framework for connecting a data signal with a model in a way that minimizes the required coupling yet allows the estimation of unknown parameters in the model. The need to evaluate unknown parameters in models of nonlinear physical, biophysical, and engineering systems occurs throughout the development of phenomenological or reduced models of dynamics. Our approach builds on existing work that uses synchronization as a tool for parameter estimation. We address some of the critical issues in that work and provide a practical framework for finding an accurate solution. In particular, we show the equivalence of this problem to that of tracking within an optimal control framework. This equivalence allows the application of powerful numerical methods that provide robust practical tools for model development and validation

  2. Group-invariant solutions of nonlinear elastodynamic problems of plates and shells

    International Nuclear Information System (INIS)

    Dzhupanov, V.A.; Vassilev, V.M.; Dzhondzhorov, P.A.

    1993-01-01

    Plates and shells are basic structural components in nuclear reactors and their equipment. The prediction of the dynamic response of these components to fast transient loadings (e.g., loadings caused by earthquakes, missile impacts, etc.) is a quite important problem in the general context of the design, reliability and safety of nuclear power stations. Due to the extreme loading conditions a more adequate treatment of the foregoing problem should rest on a suitable nonlinear shell model, which would allow large deflections of the structures regarded to be taken into account. Such a model is provided in the nonlinear Donnell-Mushtari-Vlasov (DMV) theory. The governing system of equations of the DMV theory consists of two coupled nonlinear fourth order partial differential equations in three independent and two dependent variables. It is clear, as the case stands, that the obtaining solutions to this system directly, by using any of the general analytical or numerical techniques, would involve considerable difficulties. In the present paper, the invariance of the governing equations of DMV theory for plates and cylindrical shells relative to local Lie groups of local point transformations will be employed to get some advantages in connection with the aforementioned problem. First, the symmetry of a functional, corresponding to the governing equations of DMV theory for plates and cylindrical shells is studied. Next, the densities in the corresponding conservation laws are determined on the basis of Noether theorem. Finally, we study a class of invariant solutions of the governing equations. As is well known, group-invariant solutions are often intermediate asymptotics for a wider class of solutions of the corresponding equations. When such solutions are considered, the number of the independent variables can be reduced. For the class of invariant solutions studied here, the system of governing equations converts into a system of ordinary differential equations

  3. On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation

    Directory of Open Access Journals (Sweden)

    Mesloub Said

    2008-01-01

    Full Text Available This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the existence and uniqueness of solutions in a weighted Sobolev space. Proofs are based on some a priori estimates and on the Schauder fixed point theorem. we also give a result which helps to establish the regularity of a solution.

  4. Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations

    Directory of Open Access Journals (Sweden)

    M. G. Crandall

    1999-07-01

    Full Text Available We study existence of continuous weak (viscosity solutions of Dirichlet and Cauchy-Dirichlet problems for fully nonlinear uniformly elliptic and parabolic equations. Two types of results are obtained in contexts where uniqueness of solutions fails or is unknown. For equations with merely measurable coefficients we prove solvability of the problem, while in the continuous case we construct maximal and minimal solutions. Necessary barriers on external cones are also constructed.

  5. On the solvability of initial-value problems for nonlinear implicit difference equations

    Directory of Open Access Journals (Sweden)

    Ha Thi Ngoc Yen

    2004-07-01

    Full Text Available Our aim is twofold. First, we propose a natural definition of index for linear nonautonomous implicit difference equations, which is similar to that of linear differential-algebraic equations. Then we extend this index notion to a class of nonlinear implicit difference equations and prove some existence theorems for their initial-value problems.

  6. Exact solution to the problem of nonlinear pulse propagation through random layered media and its connection with number triangles

    International Nuclear Information System (INIS)

    Sokolow, Adam; Sen, Surajit

    2007-01-01

    An energy pulse refers to a spatially compact energy bundle. In nonlinear pulse propagation, the nonlinearity of the relevant dynamical equations could lead to pulse propagation that is nondispersive or weakly dispersive in space and time. Nonlinear pulse propagation through layered media with widely varying pulse transmission properties is not wave-like and a problem of broad interest in many areas such as optics, geophysics, atmospheric physics and ocean sciences. We study nonlinear pulse propagation through a semi-infinite sequence of layers where the layers can have arbitrary energy transmission properties. By assuming that the layers are rigid, we are able to develop exact expressions for the backscattered energy received at the surface layer. The present study is likely to be relevant in the context of energy transport through soil and similar complex media. Our study reveals a surprising connection between the problem of pulse propagation and the number patterns in the well known Pascal's and Catalan's triangles and hence provides an analytic benchmark in a challenging problem of broad interest. We close with comments on the relationship between this study and the vast body of literature on the problem of wave localization in disordered systems

  7. Admissible solutions for a class of nonlinear parabolic problem with non-negative data

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Petzeltová, Hana; Simondon, F.

    2001-01-01

    Roč. 131, č. 5 (2001), s. 857-883 ISSN 0308-2105 R&D Projects: GA AV ČR IAA1019703 Keywords : admissible solutions%nonlinear parabolic problem * admissible solutions * comparison principle * non-negative data Subject RIV: BA - General Mathematics Impact factor: 0.441, year: 2001

  8. Neural networks for feedback feedforward nonlinear control systems.

    Science.gov (United States)

    Parisini, T; Zoppoli, R

    1994-01-01

    This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method.

  9. Solving non-linear Horn clauses using a linear Horn clause solver

    DEFF Research Database (Denmark)

    Kafle, Bishoksan; Gallagher, John Patrick; Ganty, Pierre

    2016-01-01

    In this paper we show that checking satisfiability of a set of non-linear Horn clauses (also called a non-linear Horn clause program) can be achieved using a solver for linear Horn clauses. We achieve this by interleaving a program transformation with a satisfiability checker for linear Horn...... clauses (also called a solver for linear Horn clauses). The program transformation is based on the notion of tree dimension, which we apply to a set of non-linear clauses, yielding a set whose derivation trees have bounded dimension. Such a set of clauses can be linearised. The main algorithm...... dimension. We constructed a prototype implementation of this approach and performed some experiments on a set of verification problems, which shows some promise....

  10. Iterative Methods for Solving Nonlinear Parabolic Problem in Pension Saving Management

    Science.gov (United States)

    Koleva, M. N.

    2011-11-01

    In this work we consider a nonlinear parabolic equation, obtained from Riccati like transformation of the Hamilton-Jacobi-Bellman equation, arising in pension saving management. We discuss two numerical iterative methods for solving the model problem—fully implicit Picard method and mixed Picard-Newton method, which preserves the parabolic characteristics of the differential problem. Numerical experiments for comparison the accuracy and effectiveness of the algorithms are discussed. Finally, observations are given.

  11. Comparative Study of Evolutionary Multi-objective Optimization Algorithms for a Non-linear Greenhouse Climate Control Problem

    DEFF Research Database (Denmark)

    Ghoreishi, Newsha; Sørensen, Jan Corfixen; Jørgensen, Bo Nørregaard

    2015-01-01

    Non-trivial real world decision-making processes usually involve multiple parties having potentially conflicting interests over a set of issues. State-of-the-art multi-objective evolutionary algorithms (MOEA) are well known to solve this class of complex real-world problems. In this paper, we...... compare the performance of state-of-the-art multi-objective evolutionary algorithms to solve a non-linear multi-objective multi-issue optimisation problem found in Greenhouse climate control. The chosen algorithms in the study includes NSGAII, eNSGAII, eMOEA, PAES, PESAII and SPEAII. The performance...... of all aforementioned algorithms is assessed and compared using performance indicators to evaluate proximity, diversity and consistency. Our insights to this comparative study enhanced our understanding of MOEAs performance in order to solve a non-linear complex climate control problem. The empirical...

  12. Probabilistic analysis of a materially nonlinear structure

    Science.gov (United States)

    Millwater, H. R.; Wu, Y.-T.; Fossum, A. F.

    1990-01-01

    A probabilistic finite element program is used to perform probabilistic analysis of a materially nonlinear structure. The program used in this study is NESSUS (Numerical Evaluation of Stochastic Structure Under Stress), under development at Southwest Research Institute. The cumulative distribution function (CDF) of the radial stress of a thick-walled cylinder under internal pressure is computed and compared with the analytical solution. In addition, sensitivity factors showing the relative importance of the input random variables are calculated. Significant plasticity is present in this problem and has a pronounced effect on the probabilistic results. The random input variables are the material yield stress and internal pressure with Weibull and normal distributions, respectively. The results verify the ability of NESSUS to compute the CDF and sensitivity factors of a materially nonlinear structure. In addition, the ability of the Advanced Mean Value (AMV) procedure to assess the probabilistic behavior of structures which exhibit a highly nonlinear response is shown. Thus, the AMV procedure can be applied with confidence to other structures which exhibit nonlinear behavior.

  13. Modeling of non-linear CHP efficiency curves in distributed energy systems

    DEFF Research Database (Denmark)

    Milan, Christian; Stadler, Michael; Cardoso, Gonçalo

    2015-01-01

    Distributed energy resources gain an increased importance in commercial and industrial building design. Combined heat and power (CHP) units are considered as one of the key technologies for cost and emission reduction in buildings. In order to make optimal decisions on investment and operation...... for these technologies, detailed system models are needed. These models are often formulated as linear programming problems to keep computational costs and complexity in a reasonable range. However, CHP systems involve variations of the efficiency for large nameplate capacity ranges and in case of part load operation......, which can be even of non-linear nature. Since considering these characteristics would turn the models into non-linear problems, in most cases only constant efficiencies are assumed. This paper proposes possible solutions to address this issue. For a mixed integer linear programming problem two...

  14. Fault detection for nonlinear systems - A standard problem approach

    DEFF Research Database (Denmark)

    Stoustrup, Jakob; Niemann, Hans Henrik

    1998-01-01

    The paper describes a general method for designing (nonlinear) fault detection and isolation (FDI) systems for nonlinear processes. For a rich class of nonlinear systems, a nonlinear FDI system can be designed using convex optimization procedures. The proposed method is a natural extension...

  15. Nonlinear Eigenvalue Problems in Elliptic Variational Inequalities: a local study

    International Nuclear Information System (INIS)

    Conrad, F.; Brauner, C.; Issard-Roch, F.; Nicolaenko, B.

    1985-01-01

    The authors consider a class of Nonlinear Eigenvalue Problems (N.L.E.P.) associated with Elliptic Variational Inequalities (E.V.I.). First the authors introduce the main tools for a local study of branches of solutions; the authors extend the linearization process required in the case of equations. Next the authors prove the existence of arcs of solutions close to regular vs singular points, and determine their local behavior up to the first order. Finally, the authors discuss the connection between their regularity condition and some stability concept. 37 references, 6 figures

  16. DISPL-1, 2. Order Nonlinear Partial Differential Equation System Solution for Kinetics Diffusion Problems

    International Nuclear Information System (INIS)

    Leaf, G.K.; Minkoff, M.

    1982-01-01

    1 - Description of problem or function: DISPL1 is a software package for solving second-order nonlinear systems of partial differential equations including parabolic, elliptic, hyperbolic, and some mixed types. The package is designed primarily for chemical kinetics- diffusion problems, although not limited to these problems. Fairly general nonlinear boundary conditions are allowed as well as inter- face conditions for problems in an inhomogeneous medium. The spatial domain is one- or two-dimensional with rectangular Cartesian, cylindrical, or spherical (in one dimension only) geometry. 2 - Method of solution: The numerical method is based on the use of Galerkin's procedure combined with the use of B-Splines (C.W.R. de-Boor's B-spline package) to generate a system of ordinary differential equations. These equations are solved by a sophisticated ODE software package which is a modified version of Hindmarsh's GEAR package, NESC Abstract 592. 3 - Restrictions on the complexity of the problem: The spatial domain must be rectangular with sides parallel to the coordinate geometry. Cross derivative terms are not permitted in the PDE. The order of the B-Splines is at most 12. Other parameters such as the number of mesh points in each coordinate direction, the number of PDE's etc. are set in a macro table used by the MORTRAn2 preprocessor in generating the object code

  17. New implementation method for essential boundary condition to extended element-free Galerkin method. Application to nonlinear problem

    International Nuclear Information System (INIS)

    Saitoh, Ayumu; Matsui, Nobuyuki; Itoh, Taku; Kamitani, Atsushi; Nakamura, Hiroaki

    2011-01-01

    A new method has been proposed for implementing essential boundary conditions to the Element-Free Galerkin Method (EFGM) without using the Lagrange multiplier. Furthermore, the performance of the proposed method has been investigated for a nonlinear Poisson problem. The results of computations show that, as interpolation functions become closer to delta functions, the accuracy of the solution is improved on the boundary. In addition, the accuracy of the proposed method is higher than that of the conventional EFGM. Therefore, it might be concluded that the proposed method is useful for solving the nonlinear Poisson problem. (author)

  18. Continuous reformulations for zero-one programming problems

    OpenAIRE

    Marianna De Santis; Francesco Rinaldi

    2010-01-01

    In this work, we study continuous reformulations of zero-one programming problems. We prove that, under suitable conditions, the optimal solutions of a zero-one programming problem can be obtained by solving a specific continuous problem.

  19. Semi-analog Monte Carlo (SMC) method for time-dependent non-linear three-dimensional heterogeneous radiative transfer problems

    International Nuclear Information System (INIS)

    Yun, Sung Hwan

    2004-02-01

    Radiative transfer is a complex phenomenon in which radiation field interacts with material. This thermal radiative transfer phenomenon is composed of two equations which are the balance equation of photons and the material energy balance equation. The two equations involve non-linearity due to the temperature and that makes the radiative transfer equation more difficult to solve. During the last several years, there have been many efforts to solve the non-linear radiative transfer problems by Monte Carlo method. Among them, it is known that Semi-Analog Monte Carlo (SMC) method developed by Ahrens and Larsen is accurate regard-less of the time step size in low temperature region. But their works are limited to one-dimensional, low temperature problems. In this thesis, we suggest some method to remove their limitations in the SMC method and apply to the more realistic problems. An initially cold problem was solved over entire temperature region by using piecewise linear interpolation of the heat capacity, while heat capacity is still fitted as a cubic curve within the lowest temperature region. If we assume the heat capacity to be linear in each temperature region, the non-linearity still remains in the radiative transfer equations. We then introduce the first-order Taylor expansion to linearize the non-linear radiative transfer equations. During the linearization procedure, absorption-reemission phenomena may be described by a conventional reemission time sampling scheme which is similar to the repetitive sampling scheme in particle transport Monte Carlo method. But this scheme causes significant stochastic errors, which necessitates many histories. Thus, we present a new reemission time sampling scheme which reduces stochastic errors by storing the information of absorption times. The results of the comparison of the two schemes show that the new scheme has less stochastic errors. Therefore, the improved SMC method is able to solve more realistic problems with

  20. Programming for Sparse Minimax Optimization

    DEFF Research Database (Denmark)

    Jonasson, K.; Madsen, Kaj

    1994-01-01

    We present an algorithm for nonlinear minimax optimization which is well suited for large and sparse problems. The method is based on trust regions and sequential linear programming. On each iteration, a linear minimax problem is solved for a basic step. If necessary, this is followed...... by the determination of a minimum norm corrective step based on a first-order Taylor approximation. No Hessian information needs to be stored. Global convergence is proved. This new method has been extensively tested and compared with other methods, including two well known codes for nonlinear programming...

  1. Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations

    Czech Academy of Sciences Publication Activity Database

    Dilna, N.; Rontó, András

    2010-01-01

    Roč. 60, č. 3 (2010), s. 327-338 ISSN 0139-9918 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : non-linear boundary value-problem * functional differential equation * non-local condition * unique solvability * differential inequality Subject RIV: BA - General Mathematics Impact factor: 0.316, year: 2010 http://link.springer.com/article/10.2478%2Fs12175-010-0015-9

  2. Computer programs for nonlinear algebraic equations

    International Nuclear Information System (INIS)

    Asaoka, Takumi

    1977-10-01

    We have provided principal computer subroutines for obtaining numerical solutions of nonlinear algebraic equations through a review of the various methods. Benchmark tests were performed on these subroutines to grasp the characteristics of them compared to the existing subroutines. As computer programs based on the secant method, subroutines of the Muller's method using the Chambers' algorithm were newly developed, in addition to the equipment of subroutines of the Muller's method itself. The programs based on the Muller-Chambers' method are useful especially for low-order polynomials with complex coefficients except for the case of finding the triple roots, three close roots etc. In addition, we have equipped subroutines based on the Madsen's algorithm, a variant of the Newton's method. The subroutines have revealed themselves very useful as standard programs because all the roots are found accurately for every case though they take longer computing time than other subroutines for low-order polynomials. It is shown also that an existing subroutine of the Bairstow's method gives the fastest algorithm for polynomials with complex coefficients, except for the case of finding the triple roots etc. We have provided also subroutines to estimate error bounds for all the roots produced with the various algorithms. (auth.)

  3. On Nonlinear Inverse Problems of Heat Transfer with Radiation Boundary Conditions: Application to Dehydration of Gypsum Plasterboards Exposed to Fire

    OpenAIRE

    Belmiloudi, A.; Mahé, F.

    2014-01-01

    International audience; The paper investigates boundary optimal controls and parameter estimates to the well-posedness nonlinear model of dehydration of thermic problems. We summarize the general formulations for the boundary control for initial-boundary value problem for nonlinear partial differential equations modeling the heat transfer and derive necessary optimality conditions, including the adjoint equation, for the optimal set of parameters minimizing objective functions J. Numerical si...

  4. A Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise

    KAUST Repository

    Clason, Christian

    2012-01-01

    This work is concerned with nonlinear parameter identification in partial differential equations subject to impulsive noise. To cope with the non-Gaussian nature of the noise, we consider a model with L 1 fitting. However, the nonsmoothness of the problem makes its efficient numerical solution challenging. By approximating this problem using a family of smoothed functionals, a semismooth Newton method becomes applicable. In particular, its superlinear convergence is proved under a second-order condition. The convergence of the solution to the approximating problem as the smoothing parameter goes to zero is shown. A strategy for adaptively selecting the regularization parameter based on a balancing principle is suggested. The efficiency of the method is illustrated on several benchmark inverse problems of recovering coefficients in elliptic differential equations, for which one- and two-dimensional numerical examples are presented. © by SIAM.

  5. Nonlinear problems of the theory of heterogeneous slightly curved shells

    Science.gov (United States)

    Kantor, B. Y.

    1973-01-01

    An account if given of the variational method of the solution of physically and geometrically nonlinear problems of the theory of heterogeneous slightly curved shells. Examined are the bending and supercritical behavior of plates and conical and spherical cupolas of variable thickness in a temperature field, taking into account the dependence of the elastic parameters on temperature. The bending, stability in general and load-bearing capacity of flexible isotropic elastic-plastic shells with different criteria of plasticity, taking into account compressibility and hardening. The effect of the plastic heterogeneity caused by heat treatment, surface work hardening and irradiation by fast neutron flux is investigated. Some problems of the dynamic behavior of flexible shells are solved. Calculations are performed in high approximations. Considerable attention is given to the construction of a machine algorithm and to the checking of the convergence of iterative processes.

  6. POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS

    Directory of Open Access Journals (Sweden)

    FAOUZI HADDOUCHI

    2015-11-01

    Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.

  7. Efficient Output Solution for Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences

    Directory of Open Access Journals (Sweden)

    Sie Long Kek

    2015-01-01

    Full Text Available A computational approach is proposed for solving the discrete time nonlinear stochastic optimal control problem. Our aim is to obtain the optimal output solution of the original optimal control problem through solving the simplified model-based optimal control problem iteratively. In our approach, the adjusted parameters are introduced into the model used such that the differences between the real system and the model used can be computed. Particularly, system optimization and parameter estimation are integrated interactively. On the other hand, the output is measured from the real plant and is fed back into the parameter estimation problem to establish a matching scheme. During the calculation procedure, the iterative solution is updated in order to approximate the true optimal solution of the original optimal control problem despite model-reality differences. For illustration, a wastewater treatment problem is studied and the results show the efficiency of the approach proposed.

  8. A parallel multi-domain solution methodology applied to nonlinear thermal transport problems in nuclear fuel pins

    Energy Technology Data Exchange (ETDEWEB)

    Philip, Bobby, E-mail: philipb@ornl.gov [Oak Ridge National Laboratory, One Bethel Valley Road, Oak Ridge, TN 37831 (United States); Berrill, Mark A.; Allu, Srikanth; Hamilton, Steven P.; Sampath, Rahul S.; Clarno, Kevin T. [Oak Ridge National Laboratory, One Bethel Valley Road, Oak Ridge, TN 37831 (United States); Dilts, Gary A. [Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM 87545 (United States)

    2015-04-01

    This paper describes an efficient and nonlinearly consistent parallel solution methodology for solving coupled nonlinear thermal transport problems that occur in nuclear reactor applications over hundreds of individual 3D physical subdomains. Efficiency is obtained by leveraging knowledge of the physical domains, the physics on individual domains, and the couplings between them for preconditioning within a Jacobian Free Newton Krylov method. Details of the computational infrastructure that enabled this work, namely the open source Advanced Multi-Physics (AMP) package developed by the authors is described. Details of verification and validation experiments, and parallel performance analysis in weak and strong scaling studies demonstrating the achieved efficiency of the algorithm are presented. Furthermore, numerical experiments demonstrate that the preconditioner developed is independent of the number of fuel subdomains in a fuel rod, which is particularly important when simulating different types of fuel rods. Finally, we demonstrate the power of the coupling methodology by considering problems with couplings between surface and volume physics and coupling of nonlinear thermal transport in fuel rods to an external radiation transport code.

  9. Positive solutions for a nonlinear periodic boundary-value problem with a parameter

    Directory of Open Access Journals (Sweden)

    Jingliang Qiu

    2012-08-01

    Full Text Available Using topological degree theory with a partially ordered structure of space, sufficient conditions for the existence and multiplicity of positive solutions for a second-order nonlinear periodic boundary-value problem are established. Inspired by ideas in Guo and Lakshmikantham [6], we study the dependence of positive periodic solutions as a parameter approaches infinity, $$ lim_{lambdao +infty}|x_{lambda}|=+infty,quadhbox{or}quad lim_{lambdao+infty}|x_{lambda}|=0. $$

  10. Numerical solution of large nonlinear boundary value problems by quadratic minimization techniques

    International Nuclear Information System (INIS)

    Glowinski, R.; Le Tallec, P.

    1984-01-01

    The objective of this paper is to describe the numerical treatment of large highly nonlinear two or three dimensional boundary value problems by quadratic minimization techniques. In all the different situations where these techniques were applied, the methodology remains the same and is organized as follows: 1) derive a variational formulation of the original boundary value problem, and approximate it by Galerkin methods; 2) transform this variational formulation into a quadratic minimization problem (least squares methods) or into a sequence of quadratic minimization problems (augmented lagrangian decomposition); 3) solve each quadratic minimization problem by a conjugate gradient method with preconditioning, the preconditioning matrix being sparse, positive definite, and fixed once for all in the iterative process. This paper will illustrate the methodology above on two different examples: the description of least squares solution methods and their application to the solution of the unsteady Navier-Stokes equations for incompressible viscous fluids; the description of augmented lagrangian decomposition techniques and their application to the solution of equilibrium problems in finite elasticity

  11. Eigenvalue problems for degenerate nonlinear elliptic equations in anisotropic media

    Directory of Open Access Journals (Sweden)

    Vicenţiu RăDulescu

    2005-06-01

    Full Text Available We study nonlinear eigenvalue problems of the type −div(a(x∇u=g(λ,x,u in ℝN, where a(x is a degenerate nonnegative weight. We establish the existence of solutions and we obtain information on qualitative properties as multiplicity and location of solutions. Our approach is based on the critical point theory in Sobolev weighted spaces combined with a Caffarelli-Kohn-Nirenberg-type inequality. A specific minimax method is developed without making use of Palais-Smale condition.

  12. Existence of solutions for quasistatic problems of unilateral contact with nonlocal friction for nonlinear elastic materials

    Directory of Open Access Journals (Sweden)

    Alain Mignot

    2005-09-01

    Full Text Available This paper shows the existence of a solution of the quasi-static unilateral contact problem with nonlocal friction law for nonlinear elastic materials. We set up a variational incremental problem which admits a solution, when the friction coefficient is small enough, and then by passing to the limit with respect to time we obtain a solution.

  13. Sensitivity analysis in optimization and reliability problems

    International Nuclear Information System (INIS)

    Castillo, Enrique; Minguez, Roberto; Castillo, Carmen

    2008-01-01

    The paper starts giving the main results that allow a sensitivity analysis to be performed in a general optimization problem, including sensitivities of the objective function, the primal and the dual variables with respect to data. In particular, general results are given for non-linear programming, and closed formulas for linear programming problems are supplied. Next, the methods are applied to a collection of civil engineering reliability problems, which includes a bridge crane, a retaining wall and a composite breakwater. Finally, the sensitivity analysis formulas are extended to calculus of variations problems and a slope stability problem is used to illustrate the methods

  14. Sensitivity analysis in optimization and reliability problems

    Energy Technology Data Exchange (ETDEWEB)

    Castillo, Enrique [Department of Applied Mathematics and Computational Sciences, University of Cantabria, Avda. Castros s/n., 39005 Santander (Spain)], E-mail: castie@unican.es; Minguez, Roberto [Department of Applied Mathematics, University of Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: roberto.minguez@uclm.es; Castillo, Carmen [Department of Civil Engineering, University of Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: mariacarmen.castillo@uclm.es

    2008-12-15

    The paper starts giving the main results that allow a sensitivity analysis to be performed in a general optimization problem, including sensitivities of the objective function, the primal and the dual variables with respect to data. In particular, general results are given for non-linear programming, and closed formulas for linear programming problems are supplied. Next, the methods are applied to a collection of civil engineering reliability problems, which includes a bridge crane, a retaining wall and a composite breakwater. Finally, the sensitivity analysis formulas are extended to calculus of variations problems and a slope stability problem is used to illustrate the methods.

  15. A comparison of two efficient nonlinear heat conduction methodologies using a two-dimensional time-dependent benchmark problem

    International Nuclear Information System (INIS)

    Wilson, G.L.; Rydin, R.A.; Orivuori, S.

    1988-01-01

    Two highly efficient nonlinear time-dependent heat conduction methodologies, the nonlinear time-dependent nodal integral technique (NTDNT) and IVOHEAT are compared using one- and two-dimensional time-dependent benchmark problems. The NTDNT is completely based on newly developed time-dependent nodal integral methods, whereas IVOHEAT is based on finite elements in space and Crank-Nicholson finite differences in time. IVOHEAT contains the geometric flexibility of the finite element approach, whereas the nodal integral method is constrained at present to Cartesian geometry. For test problems where both methods are equally applicable, the nodal integral method is approximately six times more efficient per dimension than IVOHEAT when a comparable overall accuracy is chosen. This translates to a factor of 200 for a three-dimensional problem having relatively homogeneous regions, and to a smaller advantage as the degree of heterogeneity increases

  16. Library of problem-oriented programs for solving problems of atomic and nuclear physics

    International Nuclear Information System (INIS)

    Kharitonov, Yu.I.

    1976-01-01

    The Data Centre of the Leningrad Institute of Nuclear Physics (LIYaF) is working on the establishment of a library of problem-oriented computer programs for solving problems of atomic and nuclear physics. This paper lists and describes briefly the programs presently available to the Data Centre. The descriptions include the program code numbers, the program language, the translator for which the program is designed, and the program scope

  17. On the solvability of asymmetric quasilinear finite element approximate problems in nonlinear incompressible elasticity

    International Nuclear Information System (INIS)

    Ruas, V.

    1982-09-01

    A class of simplicial finite elements for solving incompressible elasticity problems in n-dimensional space, n=2 or 3, is presented. An asymmetric structure of the shape functions with respect to the centroid of the simplex, renders them particularly stable in the large strain case, in which the incompressibility condition is nonlinear. It is proved that under certain assembling conditions of the elements, there exists a solution to the corresponding discrete problems. Numerical examples illustrate the efficiency of the method. (Author) [pt

  18. Model Predictive Control of a Nonlinear System with Known Scheduling Variable

    DEFF Research Database (Denmark)

    Mirzaei, Mahmood; Poulsen, Niels Kjølstad; Niemann, Hans Henrik

    2012-01-01

    Model predictive control (MPC) of a class of nonlinear systems is considered in this paper. We will use Linear Parameter Varying (LPV) model of the nonlinear system. By taking the advantage of having future values of the scheduling variable, we will simplify state prediction. Consequently...... the control problem of the nonlinear system is simplied into a quadratic programming. Wind turbine is chosen as the case study and we choose wind speed as the scheduling variable. Wind speed is measurable ahead of the turbine, therefore the scheduling variable is known for the entire prediction horizon....

  19. Solution of the nonlinear inverse scattering problem by T-matrix completion. I. Theory.

    Science.gov (United States)

    Levinson, Howard W; Markel, Vadim A

    2016-10-01

    We propose a conceptually different method for solving nonlinear inverse scattering problems (ISPs) such as are commonly encountered in tomographic ultrasound imaging, seismology, and other applications. The method is inspired by the theory of nonlocality of physical interactions and utilizes the relevant formalism. We formulate the ISP as a problem whose goal is to determine an unknown interaction potential V from external scattering data. Although we seek a local (diagonally dominated) V as the solution to the posed problem, we allow V to be nonlocal at the intermediate stages of iterations. This allows us to utilize the one-to-one correspondence between V and the T matrix of the problem. Here it is important to realize that not every T corresponds to a diagonal V and we, therefore, relax the usual condition of strict diagonality (locality) of V. An iterative algorithm is proposed in which we seek T that is (i) compatible with the measured scattering data and (ii) corresponds to an interaction potential V that is as diagonally dominated as possible. We refer to this algorithm as to the data-compatible T-matrix completion. This paper is Part I in a two-part series and contains theory only. Numerical examples of image reconstruction in a strongly nonlinear regime are given in Part II [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043318 (2016)10.1103/PhysRevE.94.043318]. The method described in this paper is particularly well suited for very large data sets that become increasingly available with the use of modern measurement techniques and instrumentation.

  20. Improve Problem Solving Skills through Adapting Programming Tools

    Science.gov (United States)

    Shaykhian, Linda H.; Shaykhian, Gholam Ali

    2007-01-01

    There are numerous ways for engineers and students to become better problem-solvers. The use of command line and visual programming tools can help to model a problem and formulate a solution through visualization. The analysis of problem attributes and constraints provide insight into the scope and complexity of the problem. The visualization aspect of the problem-solving approach tends to make students and engineers more systematic in their thought process and help them catch errors before proceeding too far in the wrong direction. The problem-solver identifies and defines important terms, variables, rules, and procedures required for solving a problem. Every step required to construct the problem solution can be defined in program commands that produce intermediate output. This paper advocates improved problem solving skills through using a programming tool. MatLab created by MathWorks, is an interactive numerical computing environment and programming language. It is a matrix-based system that easily lends itself to matrix manipulation, and plotting of functions and data. MatLab can be used as an interactive command line or a sequence of commands that can be saved in a file as a script or named functions. Prior programming experience is not required to use MatLab commands. The GNU Octave, part of the GNU project, a free computer program for performing numerical computations, is comparable to MatLab. MatLab visual and command programming are presented here.

  1. Near-optimal alternative generation using modified hit-and-run sampling for non-linear, non-convex problems

    Science.gov (United States)

    Rosenberg, D. E.; Alafifi, A.

    2016-12-01

    Water resources systems analysis often focuses on finding optimal solutions. Yet an optimal solution is optimal only for the modelled issues and managers often seek near-optimal alternatives that address un-modelled objectives, preferences, limits, uncertainties, and other issues. Early on, Modelling to Generate Alternatives (MGA) formalized near-optimal as the region comprising the original problem constraints plus a new constraint that allowed performance within a specified tolerance of the optimal objective function value. MGA identified a few maximally-different alternatives from the near-optimal region. Subsequent work applied Markov Chain Monte Carlo (MCMC) sampling to generate a larger number of alternatives that span the near-optimal region of linear problems or select portions for non-linear problems. We extend the MCMC Hit-And-Run method to generate alternatives that span the full extent of the near-optimal region for non-linear, non-convex problems. First, start at a feasible hit point within the near-optimal region, then run a random distance in a random direction to a new hit point. Next, repeat until generating the desired number of alternatives. The key step at each iterate is to run a random distance along the line in the specified direction to a new hit point. If linear equity constraints exist, we construct an orthogonal basis and use a null space transformation to confine hits and runs to a lower-dimensional space. Linear inequity constraints define the convex bounds on the line that runs through the current hit point in the specified direction. We then use slice sampling to identify a new hit point along the line within bounds defined by the non-linear inequity constraints. This technique is computationally efficient compared to prior near-optimal alternative generation techniques such MGA, MCMC Metropolis-Hastings, evolutionary, or firefly algorithms because search at each iteration is confined to the hit line, the algorithm can move in one

  2. Nonlinear wave equations

    CERN Document Server

    Li, Tatsien

    2017-01-01

    This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.

  3. A Hartman–Nagumo inequality for the vector ordinary -Laplacian and applications to nonlinear boundary value problems

    Directory of Open Access Journals (Sweden)

    Ureña Antonio J

    2002-01-01

    Full Text Available A generalization of the well-known Hartman–Nagumo inequality to the case of the vector ordinary -Laplacian and classical degree theory provide existence results for some associated nonlinear boundary value problems.

  4. Nonlinear Preconditioning and its Application in Multicomponent Problems

    KAUST Repository

    Liu, Lulu

    2015-01-01

    the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partitioning of degrees of freedom in a nonlinear PDE system by field type rather than by subdomain, where a modest

  5. Relaxation and decomposition methods for mixed integer nonlinear programming

    CERN Document Server

    Nowak, Ivo; Bank, RE

    2005-01-01

    This book presents a comprehensive description of efficient methods for solving nonconvex mixed integer nonlinear programs, including several numerical and theoretical results, which are presented here for the first time. It contains many illustrations and an up-to-date bibliography. Because on the emphasis on practical methods, as well as the introduction into the basic theory, the book is accessible to a wide audience. It can be used both as a research and as a graduate text.

  6. Large-scale sequential quadratic programming algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Eldersveld, S.K.

    1992-09-01

    The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.

  7. Nonlinear dynamics and plasma transport

    International Nuclear Information System (INIS)

    Liu, C.S.; Sagdeev, R.; Antonsen, T.; Drake, J.; Hassma, A.; Guzdar, P.N.

    1995-12-01

    This progress report reports work done on a program in nonlinear dynamical aspects of plasma turbulence and transport funded by DOE from 1992-1995. The purpose of this program has been to promote the utilization of recent pathbreaking developments in nonlinear science in plasma turbulence and transport and to fully utilize the scientific expertise of Russian fusion and plasma community in collaboration with our group to address outstanding fusion theory problems. In the work reported in our progress report, we have studied simple models which are motivated by observation on actual fusion devices. The models focus on the important physical processes without incorporating the complexity of the geometry of real devices. We have also studied linear stability problems which incorporated important physics issues related to geometry involving closed field lines and open field lines. This allows for a deeper analysis and understanding of the system both analytically and numerically. The strong collaboration between the Russian visitors and the US participants has led to a fruitful and strong research program that taps the complementary analytic and numerical capabilities of the two groups. Over the years several distinguished Russian visitors have interacted with various members of the group and set up collaborative work which forms a significant part of proposed research. Dr. Galeev, Director of the Space Research Institute of Moscow and Dr. Novakovskii from the Kurchatov Institute are two such ongoing collaborations. 21 refs

  8. Ensemble Kalman Filtering with Residual Nudging: An Extension to State Estimation Problems with Nonlinear Observation Operators

    KAUST Repository

    Luo, Xiaodong

    2014-10-01

    The ensemble Kalman filter (EnKF) is an efficient algorithm for many data assimilation problems. In certain circumstances, however, divergence of the EnKF might be spotted. In previous studies, the authors proposed an observation-space-based strategy, called residual nudging, to improve the stability of the EnKF when dealing with linear observation operators. The main idea behind residual nudging is to monitor and, if necessary, adjust the distances (misfits) between the real observations and the simulated ones of the state estimates, in the hope that by doing so one may be able to obtain better estimation accuracy. In the present study, residual nudging is extended and modified in order to handle nonlinear observation operators. Such extension and modification result in an iterative filtering framework that, under suitable conditions, is able to achieve the objective of residual nudging for data assimilation problems with nonlinear observation operators. The 40-dimensional Lorenz-96 model is used to illustrate the performance of the iterative filter. Numerical results show that, while a normal EnKF may diverge with nonlinear observation operators, the proposed iterative filter remains stable and leads to reasonable estimation accuracy under various experimental settings.

  9. On the Cauchy problem for a Sobolev-type equation with quadratic non-linearity

    International Nuclear Information System (INIS)

    Aristov, Anatoly I

    2011-01-01

    We investigate the asymptotic behaviour as t→∞ of the solution of the Cauchy problem for a Sobolev-type equation with quadratic non-linearity and develop ideas used by I. A. Shishmarev and other authors in the study of classical and Sobolev-type equations. Conditions are found under which it is possible to consider the case of an arbitrary dimension of the spatial variable.

  10. Positive solutions of nonlinear fractional boundary value problems with Dirichlet boundary conditions

    Directory of Open Access Journals (Sweden)

    Qingkai Kong

    2012-02-01

    Full Text Available In this paper, we study the existence and multiplicity of positive solutions of a class of nonlinear fractional boundary value problems with  Dirichlet boundary conditions. By applying the fixed point theory on cones we establish a series of criteria for the existence of one, two, any arbitrary finite number, and an infinite number of positive solutions. A criterion for the nonexistence of positive solutions is also derived. Several examples are given for demonstration.

  11. The focal boundary value problem for strongly singular higher-order nonlinear functional-differential equations

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan; Půža, B.

    2015-01-01

    Roč. 2015, January (2015), s. 17 ISSN 1687-2770 Institutional support: RVO:67985840 Keywords : higher order nonlinear functional-differential equations * two-point right-focal boundary value problem * strong singularity Subject RIV: BA - General Mathematics Impact factor: 0.642, year: 2015 http://link.springer.com/article/10.1186%2Fs13661-014-0277-1

  12. An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition

    Science.gov (United States)

    Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

    2018-06-01

    This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method.

  13. Solution of problems with material nonlinearities with a coupled finite element/boundary element scheme using an iterative solver. Yucca Mountain Site Characterization Project

    International Nuclear Information System (INIS)

    Koteras, J.R.

    1996-01-01

    The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region

  14. Application of power series to the solution of the boundary value problem for a second order nonlinear differential equation

    International Nuclear Information System (INIS)

    Semenova, V.N.

    2016-01-01

    A boundary value problem for a nonlinear second order differential equation has been considered. A numerical method has been proposed to solve this problem using power series. Results of numerical experiments have been presented in the paper [ru

  15. Optimization of lift gas allocation in a gas lifted oil field as non-linear optimization problem

    Directory of Open Access Journals (Sweden)

    Roshan Sharma

    2012-01-01

    Full Text Available Proper allocation and distribution of lift gas is necessary for maximizing total oil production from a field with gas lifted oil wells. When the supply of the lift gas is limited, the total available gas should be optimally distributed among the oil wells of the field such that the total production of oil from the field is maximized. This paper describes a non-linear optimization problem with constraints associated with the optimal distribution of the lift gas. A non-linear objective function is developed using a simple dynamic model of the oil field where the decision variables represent the lift gas flow rate set points of each oil well of the field. The lift gas optimization problem is solved using the emph'fmincon' solver found in MATLAB. As an alternative and for verification, hill climbing method is utilized for solving the optimization problem. Using both of these methods, it has been shown that after optimization, the total oil production is increased by about 4. For multiple oil wells sharing lift gas from a common source, a cascade control strategy along with a nonlinear steady state optimizer behaves as a self-optimizing control structure when the total supply of lift gas is assumed to be the only input disturbance present in the process. Simulation results show that repeated optimization performed after the first time optimization under the presence of the input disturbance has no effect in the total oil production.

  16. Neutrosophic Integer Programming Problem

    Directory of Open Access Journals (Sweden)

    Mai Mohamed

    2017-02-01

    Full Text Available In this paper, we introduce the integer programming in neutrosophic environment, by considering coffecients of problem as a triangulare neutrosophic numbers. The degrees of acceptance, indeterminacy and rejection of objectives are simultaneously considered.

  17. Uniqueness of global quasi-classical solutions of the Cauchy problems for first-order nonlinear partial differential equations

    International Nuclear Information System (INIS)

    Tran Duc Van

    1994-01-01

    The notion of global quasi-classical solutions of the Cauchy problems for first-order nonlinear partial differential equations is presented, some uniqueness theorems and a stability result are established by the method based on the theory of differential inclusions. In particular, the answer to an open problem of S.N. Kruzhkov is given. (author). 10 refs, 1 fig

  18. Multiparametric programming based algorithms for pure integer and mixed-integer bilevel programming problems

    KAUST Repository

    Domí nguez, Luis F.; Pistikopoulos, Efstratios N.

    2010-01-01

    continuous multiparametric programming algorithm is then used to solve the reformulated convex inner problem. The second algorithm addresses the mixed-integer case of the bilevel programming problem where integer and continuous variables of the outer problem

  19. Tilt stability in nonlinear programming under Mangasarian-Fromovitz constraint qualification

    Czech Academy of Sciences Publication Activity Database

    Mordukhovich, B. S.; Outrata, Jiří

    2013-01-01

    Roč. 49, č. 3 (2013), s. 446-464 ISSN 0023-5954 R&D Projects: GA ČR(CZ) GAP201/12/0671 Institutional support: RVO:67985556 Keywords : variational analysis * second-order theory * generalized differentiation * tilt stability Subject RIV: BA - General Mathematics Impact factor: 0.563, year: 2013 http://library.utia.cas.cz/separaty/2013/MTR/outrata-tilt stability in nonlinear programming under mangasarian-fromovitz constraint qualification.pdf

  20. Nonlinear dynamic analysis using Petrov-Galerkin natural element method

    International Nuclear Information System (INIS)

    Lee, Hong Woo; Cho, Jin Rae

    2004-01-01

    According to our previous study, it is confirmed that the Petrov-Galerkin Natural Element Method (PG-NEM) completely resolves the numerical integration inaccuracy in the conventional Bubnov-Galerkin Natural Element Method (BG-NEM). This paper is an extension of PG-NEM to two-dimensional nonlinear dynamic problem. For the analysis, a constant average acceleration method and a linearized total Lagrangian formulation is introduced with the PG-NEM. At every time step, the grid points are updated and the shape functions are reproduced from the relocated nodal distribution. This process enables the PG-NEM to provide more accurate and robust approximations. The representative numerical experiments performed by the test Fortran program, and the numerical results confirmed that the PG-NEM effectively and accurately approximates the nonlinear dynamic problem

  1. Multi-objective convex programming problem arising in multivariate ...

    African Journals Online (AJOL)

    user

    Multi-objective convex programming problem arising in ... However, although the consideration of multiple objectives may seem a novel concept, virtually any nontrivial ..... Solving multiobjective programming problems by discrete optimization.

  2. Spike-layer solutions to nonlinear fractional Schrodinger equations with almost optimal nonlinearities

    Directory of Open Access Journals (Sweden)

    Jinmyoung Seok

    2015-07-01

    Full Text Available In this article, we are interested in singularly perturbed nonlinear elliptic problems involving a fractional Laplacian. Under a class of nonlinearity which is believed to be almost optimal, we construct a positive solution which exhibits multiple spikes near any given local minimum components of an exterior potential of the problem.

  3. Trajectory Planning of Satellite Formation Flying using Nonlinear Programming and Collocation

    Directory of Open Access Journals (Sweden)

    Hyung-Chu Lim

    2008-12-01

    Full Text Available Recently, satellite formation flying has been a topic of significant research interest in aerospace society because it provides potential benefits compared to a large spacecraft. Some techniques have been proposed to design optimal formation trajectories minimizing fuel consumption in the process of formation configuration or reconfiguration. In this study, a method is introduced to build fuel-optimal trajectories minimizing a cost function that combines the total fuel consumption of all satellites and assignment of fuel consumption rate for each satellite. This approach is based on collocation and nonlinear programming to solve constraints for collision avoidance and the final configuration. New constraints of nonlinear equality or inequality are derived for final configuration, and nonlinear inequality constraints are established for collision avoidance. The final configuration constraints are that three or more satellites should form a projected circular orbit and make an equilateral polygon in the horizontal plane. Example scenarios, including these constraints and the cost function, are simulated by the method to generate optimal trajectories for the formation configuration and reconfiguration of multiple satellites.

  4. The genetic algorithm for the nonlinear programming of water pollution control system

    Energy Technology Data Exchange (ETDEWEB)

    Wei, J.; Zhang, J. [China University of Geosciences (China)

    1999-08-01

    In the programming of water pollution control system the combined method of optimization with simulation is used generally. It is not only laborious in calculation, but also the global optimum of the obtained solution is guaranteed difficult. In this paper, the genetic algorithm (GA) used in the nonlinear programming of water pollution control system is given, by which the preferred conception for the programming of waste water system is found in once-through operation. It is more succinct than the conventional method and the global optimum of the obtained solution could be ensured. 6 refs., 4 figs., 3 tabs.

  5. Nonlinear beam dynamics experimental program at SPEAR

    International Nuclear Information System (INIS)

    Tran, P.; Pellegrini, C.; Cornacchia, M.; Lee, M.; Corbett, W.

    1995-01-01

    Since nonlinear effects can impose strict performance limitations on modern colliders and storage rings, future performance improvements depend on further understanding of nonlinear beam dynamics. Experimental studies of nonlinear beam motion in three-dimensional space have begun in SPEAR using turn-by-turn transverse and longitudinal phase-space monitors. This paper presents preliminary results from an on-going experiment in SPEAR

  6. Studies in nonlinear problems of energy. Progress report, January 1, 1992--December 31, 1992

    Energy Technology Data Exchange (ETDEWEB)

    Matkowsky, B.J.

    1992-07-01

    Emphasis has been on combustion and flame propagation. The research program was on modeling, analysis and computation of combustion phenomena, with emphasis on transition from laminar to turbulent combustion. Nonlinear dynamics and pattern formation were investigated in the transition. Stability of combustion waves, and transitions to complex waves are described. Combustion waves possess large activation energies, so that chemical reactions are significant only in thin layers, or reaction zones. In limit of infinite activation energy, the zones shrink to moving surfaces, (fronts) which must be found during the analysis, so that (moving free boundary problems). The studies are carried out for limiting case with fronts, while the numerical studies are carried out for finite, though large, activation energy. Accurate resolution of the solution in the reaction zones is essential, otherwise false predictions of dynamics are possible. Since the the reaction zones move, adaptive pseudo-spectral methods were developed. The approach is based on a synergism of analytical and computational methods. The numerical computations build on and extend the analytical information. Furthermore, analytical solutions serve as benchmarks for testing the accuracy of the computation. Finally, ideas from analysis (singular perturbation theory) have induced new approaches to computations. The computational results suggest new analysis to be considered. Among the recent interesting results, was spatio-temporal chaos in combustion. One goal is extension of the adaptive pseudo-spectral methods to adaptive domain decomposition methods. Efforts have begun to develop such methods for problems with multiple reaction zones, corresponding to problems with more complex, and more realistic chemistry. Other topics included stochastics, oscillators, Rysteretic Josephson junctions, DC SQUID, Markov jumps, laser with saturable absorber, chemical physics, Brownian movement, combustion synthesis, etc.

  7. Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions

    Science.gov (United States)

    Lin, Yezhi; Liu, Yinping; Li, Zhibin

    2012-01-01

    The Adomian decomposition method (ADM) is one of the most effective methods for constructing analytic approximate solutions of nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, and the two-step Adomian decomposition method (TSADM) combined with the Padé technique, a new algorithm is proposed to construct accurate analytic approximations of nonlinear differential equations with initial conditions. Furthermore, a MAPLE package is developed, which is user-friendly and efficient. One only needs to input a system, initial conditions and several necessary parameters, then our package will automatically deliver analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the validity of the package. Our program provides a helpful and easy-to-use tool in science and engineering to deal with initial value problems. Program summaryProgram title: NAPA Catalogue identifier: AEJZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJZ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4060 No. of bytes in distributed program, including test data, etc.: 113 498 Distribution format: tar.gz Programming language: MAPLE R13 Computer: PC Operating system: Windows XP/7 RAM: 2 Gbytes Classification: 4.3 Nature of problem: Solve nonlinear differential equations with initial conditions. Solution method: Adomian decomposition method and Padé technique. Running time: Seconds at most in routine uses of the program. Special tasks may take up to some minutes.

  8. Analysis and monitoring of energy security and prediction of indicator values using conventional non-linear mathematical programming

    Directory of Open Access Journals (Sweden)

    Elena Vital'evna Bykova

    2011-09-01

    Full Text Available This paper describes the concept of energy security and a system of indicators for its monitoring. The indicator system includes more than 40 parameters that reflect the structure and state of fuel and energy complex sectors (fuel, electricity and heat & power, as well as takes into account economic, environmental and social aspects. A brief description of the structure of the computer system to monitor and analyze energy security is given. The complex contains informational, analytical and calculation modules, provides applications for forecasting and modeling energy scenarios, modeling threats and determining levels of energy security. Its application to predict the values of the indicators and methods developed for it are described. This paper presents a method developed by conventional nonlinear mathematical programming needed to address several problems of energy and, in particular, the prediction problem of the security. An example of its use and implementation of this method in the application, "Prognosis", is also given.

  9. Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach

    Directory of Open Access Journals (Sweden)

    S. L. Han

    2012-01-01

    Full Text Available The nonlinear model is crucial to prepare, supervise, and analyze mechanical system. In this paper, a new nonparametric and output-only identification procedure for nonlinear damping is studied. By introducing the concept of the stochastic state space, we formulate a stochastic inverse problem for a nonlinear damping. The solution of the stochastic inverse problem is designed as probabilistic expression via the hierarchical Bayesian formulation by considering various uncertainties such as the information insufficiency in parameter of interests or errors in measurement. The probability space is estimated using Markov chain Monte Carlo (MCMC. The applicability of the proposed method is demonstrated through numerical experiment and particular application to a realistic problem related to ship roll motion.

  10. Non-intrusive reduced order modeling of nonlinear problems using neural networks

    Science.gov (United States)

    Hesthaven, J. S.; Ubbiali, S.

    2018-06-01

    We develop a non-intrusive reduced basis (RB) method for parametrized steady-state partial differential equations (PDEs). The method extracts a reduced basis from a collection of high-fidelity solutions via a proper orthogonal decomposition (POD) and employs artificial neural networks (ANNs), particularly multi-layer perceptrons (MLPs), to accurately approximate the coefficients of the reduced model. The search for the optimal number of neurons and the minimum amount of training samples to avoid overfitting is carried out in the offline phase through an automatic routine, relying upon a joint use of the Latin hypercube sampling (LHS) and the Levenberg-Marquardt (LM) training algorithm. This guarantees a complete offline-online decoupling, leading to an efficient RB method - referred to as POD-NN - suitable also for general nonlinear problems with a non-affine parametric dependence. Numerical studies are presented for the nonlinear Poisson equation and for driven cavity viscous flows, modeled through the steady incompressible Navier-Stokes equations. Both physical and geometrical parametrizations are considered. Several results confirm the accuracy of the POD-NN method and show the substantial speed-up enabled at the online stage as compared to a traditional RB strategy.

  11. Solution of a few nonlinear problems in aerodynamics by the finite elements and functional least squares methods. Ph.D. Thesis - Paris Univ.; [mathematical models of transonic flow using nonlinear equations

    Science.gov (United States)

    Periaux, J.

    1979-01-01

    The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.

  12. Mathematical and numerical study of nonlinear boundary problems related to plasma physics

    International Nuclear Information System (INIS)

    Sermange, M.

    1982-06-01

    After the study of some equations based on the Hodgkin-Huxley model, the work presented here is concerned with nonlinear boundary problems in MHD. They are gathered in two subjects: equilibrium equations and stability equations. The axisymmetric MHD equilibrium equations with free boundary have been studied by different authors, particularly the existence, regularity, unicity and non-unicity. Here, bifurcation, convergence of calculation methods existence of solutions in a discontinuous frame are studied. MHD stability can be determined by the principle of Bernstein et al; the mathematical work concerned here bears on the equivalence, in the case of two-dimensional or axisymmetric stability, between this model and a scalar eigenvalue problem which is introduced. At last, modules for computing MHD equilibrium for the simulation of plasma confinement in a tokamak are described [fr

  13. A limited memory BFGS method for a nonlinear inverse problem in digital breast tomosynthesis

    Science.gov (United States)

    Landi, G.; Loli Piccolomini, E.; Nagy, J. G.

    2017-09-01

    Digital breast tomosynthesis (DBT) is an imaging technique that allows the reconstruction of a pseudo three-dimensional image of the breast from a finite number of low-dose two-dimensional projections obtained by different x-ray tube angles. An issue that is often ignored in DBT is the fact that an x-ray beam is polyenergetic, i.e. it is composed of photons with different levels of energy. The polyenergetic model requires solving a large-scale, nonlinear inverse problem, which is more expensive than the typically used simplified, linear monoenergetic model. However, the polyenergetic model is much less susceptible to beam hardening artifacts, which show up as dark streaks and cupping (i.e. background nonuniformities) in the reconstructed image. In addition, it has been shown that the polyenergetic model can be exploited to obtain additional quantitative information about the material of the object being imaged. In this paper we consider the multimaterial polyenergetic DBT model, and solve the nonlinear inverse problem with a limited memory BFGS quasi-Newton method. Regularization is enforced at each iteration using a diagonally modified approximation of the Hessian matrix, and by truncating the iterations.

  14. Nonlinear approaches in engineering applications 2

    CERN Document Server

    Jazar, Reza N

    2013-01-01

    Provides updated principles and applications of the nonlinear approaches in solving engineering and physics problems Demonstrates how nonlinear approaches may open avenues to better, safer, cheaper systems with less energy consumption Has a strong emphasis on the application, physical meaning, and methodologies of nonlinear approaches in different engineering and science problems

  15. Finite element calculations illustrating a method of model reduction for the dynamics of structures with localized nonlinearities.

    Energy Technology Data Exchange (ETDEWEB)

    Griffith, Daniel Todd; Segalman, Daniel Joseph

    2006-10-01

    A technique published in SAND Report 2006-1789 ''Model Reduction of Systems with Localized Nonlinearities'' is illustrated in two problems of finite element structural dynamics. That technique, called here the Method of Locally Discontinuous Basis Vectors (LDBV), was devised to address the peculiar difficulties of model reduction of systems having spatially localized nonlinearities. It's illustration here is on two problems of different geometric and dynamic complexity, but each containing localized interface nonlinearities represented by constitutive models for bolted joint behavior. As illustrated on simple problems in the earlier SAND report, the LDBV Method not only affords reduction in size of the nonlinear systems of equations that must be solved, but it also facilitates the use of much larger time steps on problems of joint macro-slip than would be possible otherwise. These benefits are more dramatic for the larger problems illustrated here. The work of both the original SAND report and this one were funded by the LDRD program at Sandia National Laboratories.

  16. Nonlinear dynamics of quadratically cubic systems

    International Nuclear Information System (INIS)

    Rudenko, O V

    2013-01-01

    We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg–de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space–time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed. (methodological notes)

  17. Non-linear time series extreme events and integer value problems

    CERN Document Server

    Turkman, Kamil Feridun; Zea Bermudez, Patrícia

    2014-01-01

    This book offers a useful combination of probabilistic and statistical tools for analyzing nonlinear time series. Key features of the book include a study of the extremal behavior of nonlinear time series and a comprehensive list of nonlinear models that address different aspects of nonlinearity. Several inferential methods, including quasi likelihood methods, sequential Markov Chain Monte Carlo Methods and particle filters, are also included so as to provide an overall view of the available tools for parameter estimation for nonlinear models. A chapter on integer time series models based on several thinning operations, which brings together all recent advances made in this area, is also included. Readers should have attended a prior course on linear time series, and a good grasp of simulation-based inferential methods is recommended. This book offers a valuable resource for second-year graduate students and researchers in statistics and other scientific areas who need a basic understanding of nonlinear time ...

  18. Nonlinear robust hierarchical control for nonlinear uncertain systems

    Directory of Open Access Journals (Sweden)

    Leonessa Alexander

    1999-01-01

    Full Text Available A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.

  19. Solving Boundary Value Problem for a Nonlinear Stationary Controllable System with Synthesizing Control

    Directory of Open Access Journals (Sweden)

    Alexander N. Kvitko

    2017-01-01

    Full Text Available An algorithm for constructing a control function that transfers a wide class of stationary nonlinear systems of ordinary differential equations from an initial state to a final state under certain control restrictions is proposed. The algorithm is designed to be convenient for numerical implementation. A constructive criterion of the desired transfer possibility is presented. The problem of an interorbital flight is considered as a test example and it is simulated numerically with the presented method.

  20. A goal programming procedure for solving fuzzy multiobjective fractional linear programming problems

    Directory of Open Access Journals (Sweden)

    Tunjo Perić

    2014-12-01

    Full Text Available This paper presents a modification of Pal, Moitra and Maulik's goal programming procedure for fuzzy multiobjective linear fractional programming problem solving. The proposed modification of the method allows simpler solving of economic multiple objective fractional linear programming (MOFLP problems, enabling the obtained solutions to express the preferences of the decision maker defined by the objective function weights. The proposed method is tested on the production planning example.

  1. A quasi-sequential parameter estimation for nonlinear dynamic systems based on multiple data profiles

    Energy Technology Data Exchange (ETDEWEB)

    Zhao, Chao [FuZhou University, FuZhou (China); Vu, Quoc Dong; Li, Pu [Ilmenau University of Technology, Ilmenau (Germany)

    2013-02-15

    A three-stage computation framework for solving parameter estimation problems for dynamic systems with multiple data profiles is developed. The dynamic parameter estimation problem is transformed into a nonlinear programming (NLP) problem by using collocation on finite elements. The model parameters to be estimated are treated in the upper stage by solving an NLP problem. The middle stage consists of multiple NLP problems nested in the upper stage, representing the data reconciliation step for each data profile. We use the quasi-sequential dynamic optimization approach to solve these problems. In the lower stage, the state variables and their gradients are evaluated through ntegrating the model equations. Since the second-order derivatives are not required in the computation framework this proposed method will be efficient for solving nonlinear dynamic parameter estimation problems. The computational results obtained on a parameter estimation problem for two CSTR models demonstrate the effectiveness of the proposed approach.

  2. A quasi-sequential parameter estimation for nonlinear dynamic systems based on multiple data profiles

    International Nuclear Information System (INIS)

    Zhao, Chao; Vu, Quoc Dong; Li, Pu

    2013-01-01

    A three-stage computation framework for solving parameter estimation problems for dynamic systems with multiple data profiles is developed. The dynamic parameter estimation problem is transformed into a nonlinear programming (NLP) problem by using collocation on finite elements. The model parameters to be estimated are treated in the upper stage by solving an NLP problem. The middle stage consists of multiple NLP problems nested in the upper stage, representing the data reconciliation step for each data profile. We use the quasi-sequential dynamic optimization approach to solve these problems. In the lower stage, the state variables and their gradients are evaluated through ntegrating the model equations. Since the second-order derivatives are not required in the computation framework this proposed method will be efficient for solving nonlinear dynamic parameter estimation problems. The computational results obtained on a parameter estimation problem for two CSTR models demonstrate the effectiveness of the proposed approach

  3. Behavior of the maximal solution of the Cauchy problem for some nonlinear pseudoparabolic equation as $|x|oinfty$

    Directory of Open Access Journals (Sweden)

    Tatiana Kavitova

    2012-08-01

    Full Text Available We prove a comparison principle for solutions of the Cauchy problem of the nonlinear pseudoparabolic equation $u_t=Delta u_t+ Deltavarphi(u +h(t,u$ with nonnegative bounded initial data. We show stabilization of a maximal solution to a maximal solution of the Cauchy problem for the corresponding ordinary differential equation $vartheta'(t=h(t,vartheta$ as $|x|oinfty$ under certain conditions on an initial datum.

  4. Constraint-based scheduling applying constraint programming to scheduling problems

    CERN Document Server

    Baptiste, Philippe; Nuijten, Wim

    2001-01-01

    Constraint Programming is a problem-solving paradigm that establishes a clear distinction between two pivotal aspects of a problem: (1) a precise definition of the constraints that define the problem to be solved and (2) the algorithms and heuristics enabling the selection of decisions to solve the problem. It is because of these capabilities that Constraint Programming is increasingly being employed as a problem-solving tool to solve scheduling problems. Hence the development of Constraint-Based Scheduling as a field of study. The aim of this book is to provide an overview of the most widely used Constraint-Based Scheduling techniques. Following the principles of Constraint Programming, the book consists of three distinct parts: The first chapter introduces the basic principles of Constraint Programming and provides a model of the constraints that are the most often encountered in scheduling problems. Chapters 2, 3, 4, and 5 are focused on the propagation of resource constraints, which usually are responsibl...

  5. Nonlinear crack mechanics

    International Nuclear Information System (INIS)

    Khoroshun, L.P.

    1995-01-01

    The characteristic features of the deformation and failure of actual materials in the vicinity of a crack tip are due to their physical nonlinearity in the stress-concentration zone, which is a result of plasticity, microfailure, or a nonlinear dependence of the interatomic forces on the distance. Therefore, adequate models of the failure mechanics must be nonlinear, in principle, although linear failure mechanics is applicable if the zone of nonlinear deformation is small in comparison with the crack length. Models of crack mechanics are based on analytical solutions of the problem of the stress-strain state in the vicinity of the crack. On account of the complexity of the problem, nonlinear models are bason on approximate schematic solutions. In the Leonov-Panasyuk-Dugdale nonlinear model, one of the best known, the actual two-dimensional plastic zone (the nonlinearity zone) is replaced by a narrow one-dimensional zone, which is then modeled by extending the crack with a specified normal load equal to the yield point. The condition of finite stress is applied here, and hence the length of the plastic zone is determined. As a result of this approximation, the displacement in the plastic zone at the abscissa is nonzero

  6. A METHOD FOR SOLVING LINEAR PROGRAMMING PROBLEMS WITH FUZZY PARAMETERS BASED ON MULTIOBJECTIVE LINEAR PROGRAMMING TECHNIQUE

    OpenAIRE

    M. ZANGIABADI; H. R. MALEKI

    2007-01-01

    In the real-world optimization problems, coefficients of the objective function are not known precisely and can be interpreted as fuzzy numbers. In this paper we define the concepts of optimality for linear programming problems with fuzzy parameters based on those for multiobjective linear programming problems. Then by using the concept of comparison of fuzzy numbers, we transform a linear programming problem with fuzzy parameters to a multiobjective linear programming problem. To this end, w...

  7. A study of the use of linear programming techniques to improve the performance in design optimization problems

    Science.gov (United States)

    Young, Katherine C.; Sobieszczanski-Sobieski, Jaroslaw

    1988-01-01

    This project has two objectives. The first is to determine whether linear programming techniques can improve performance when handling design optimization problems with a large number of design variables and constraints relative to the feasible directions algorithm. The second purpose is to determine whether using the Kreisselmeier-Steinhauser (KS) function to replace the constraints with one constraint will reduce the cost of total optimization. Comparisons are made using solutions obtained with linear and non-linear methods. The results indicate that there is no cost saving using the linear method or in using the KS function to replace constraints.

  8. Existence of solutions to nonlinear parabolic unilateral problems with an obstacle depending on time

    Directory of Open Access Journals (Sweden)

    Nabila Bellal

    2014-10-01

    Full Text Available Using the penalty method, we prove the existence of solutions to nonlinear parabolic unilateral problems with an obstacle depending on time. To find a solution, the original inequality is transformed into an equality by adding a positive function on the right-hand side and a complementary condition. This result can be seen as a generalization of the results by Mokrane in [11] where the obstacle is zero.

  9. Risk-Based Two-Stage Stochastic Optimization Problem of Micro-Grid Operation with Renewables and Incentive-Based Demand Response Programs

    Directory of Open Access Journals (Sweden)

    Pouria Sheikhahmadi

    2018-03-01

    Full Text Available The operation problem of a micro-grid (MG in grid-connected mode is an optimization one in which the main objective of the MG operator (MGO is to minimize the operation cost with optimal scheduling of resources and optimal trading energy with the main grid. The MGO can use incentive-based demand response programs (DRPs to pay an incentive to the consumers to change their demands in the peak hours. Moreover, the MGO forecasts the output power of renewable energy resources (RERs and models their uncertainties in its problem. In this paper, the operation problem of an MGO is modeled as a risk-based two-stage stochastic optimization problem. To model the uncertainties of RERs, two-stage stochastic programming is considered and conditional value at risk (CVaR index is used to manage the MGO’s risk-level. Moreover, the non-linear economic models of incentive-based DRPs are used by the MGO to change the peak load. The numerical studies are done to investigate the effect of incentive-based DRPs on the operation problem of the MGO. Moreover, to show the effect of the risk-averse parameter on MGO decisions, a sensitivity analysis is carried out.

  10. Discrete and continuum links to a nonlinear coupled transport problem of interacting populations

    Science.gov (United States)

    Duong, M. H.; Muntean, A.; Richardson, O. M.

    2017-07-01

    We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind are inspired by the dynamics of pedestrian flows in open spaces and are intimately connected to cross-diffusion and thermo-diffusion problems holding a variational structure. The tools we use include a suitable structure of the relative entropy controlling TV-norms, the construction of Lyapunov functionals and particular closed-form solutions to nonlinear transport equations, a hydrodynamics limiting procedure due to Philipowski, as well as the construction of numerical approximates to both the continuum limit problem in 2D and to the original interacting particle systems.

  11. Analyze the optimal solutions of optimization problems by means of fractional gradient based system using VIM

    Directory of Open Access Journals (Sweden)

    Firat Evirgen

    2016-04-01

    Full Text Available In this paper, a class of Nonlinear Programming problem is modeled with gradient based system of fractional order differential equations in Caputo's sense. To see the overlap between the equilibrium point of the fractional order dynamic system and theoptimal solution of the NLP problem in a longer timespan the Multistage Variational İteration Method isapplied. The comparisons among the multistage variational iteration method, the variationaliteration method and the fourth order Runge-Kutta method in fractional and integer order showthat fractional order model and techniques can be seen as an effective and reliable tool for finding optimal solutions of Nonlinear Programming problems.

  12. Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique

    Directory of Open Access Journals (Sweden)

    Omar Abu Arqub

    2014-01-01

    Full Text Available The purpose of this paper is to present a new kind of analytical method, the so-called residual power series, to predict and represent the multiplicity of solutions to nonlinear boundary value problems of fractional order. The present method is capable of calculating all branches of solutions simultaneously, even if these multiple solutions are very close and thus rather difficult to distinguish even by numerical techniques. To verify the computational efficiency of the designed proposed technique, two nonlinear models are performed, one of them arises in mixed convection flows and the other one arises in heat transfer, which both admit multiple solutions. The results reveal that the method is very effective, straightforward, and powerful for formulating these multiple solutions.

  13. A Nonlinear Multiobjective Bilevel Model for Minimum Cost Network Flow Problem in a Large-Scale Construction Project

    Directory of Open Access Journals (Sweden)

    Jiuping Xu

    2012-01-01

    Full Text Available The aim of this study is to deal with a minimum cost network flow problem (MCNFP in a large-scale construction project using a nonlinear multiobjective bilevel model with birandom variables. The main target of the upper level is to minimize both direct and transportation time costs. The target of the lower level is to minimize transportation costs. After an analysis of the birandom variables, an expectation multiobjective bilevel programming model with chance constraints is formulated to incorporate decision makers’ preferences. To solve the identified special conditions, an equivalent crisp model is proposed with an additional multiobjective bilevel particle swarm optimization (MOBLPSO developed to solve the model. The Shuibuya Hydropower Project is used as a real-world example to verify the proposed approach. Results and analysis are presented to highlight the performances of the MOBLPSO, which is very effective and efficient compared to a genetic algorithm and a simulated annealing algorithm.

  14. Introduction to nonlinear dispersive equations

    CERN Document Server

    Linares, Felipe

    2015-01-01

    This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introdu...

  15. Nonlinear Finite Element Analysis of a General Composite Shell

    Science.gov (United States)

    1988-12-01

    for (t) in Equation (B.15) (Appendix B) and writes it as a function of displacements for I the nonlinear problem one obtains [8] 3 29 (*(a)) - [K(a...linked to the main program before execution. Isubroutine upress(t,pa,pb,iunit, ielt ,x,y,z,live,press) c c Pressure distribution subroutine for c...then compiled and linked to the main program before execution. I SUBROUTINE UPRESS(T,PA,PB,IUNIT, IELT ,X,Y,Z,LIVE,PRESS) C c Pressure distribution

  16. [On the problems of the evolutionary optimization of life history. II. To justification of optimization criterion for nonlinear Leslie model].

    Science.gov (United States)

    Pasekov, V P

    2013-03-01

    The paper considers the problems in the adaptive evolution of life-history traits for individuals in the nonlinear Leslie model of age-structured population. The possibility to predict adaptation results as the values of organism's traits (properties) that provide for the maximum of a certain function of traits (optimization criterion) is studied. An ideal criterion of this type is Darwinian fitness as a characteristic of success of an individual's life history. Criticism of the optimization approach is associated with the fact that it does not take into account the changes in the environmental conditions (in a broad sense) caused by evolution, thereby leading to losses in the adequacy of the criterion. In addition, the justification for this criterion under stationary conditions is not usually rigorous. It has been suggested to overcome these objections in terms of the adaptive dynamics theory using the concept of invasive fitness. The reasons are given that favor the application of the average number of offspring for an individual, R(L), as an optimization criterion in the nonlinear Leslie model. According to the theory of quantitative genetics, the selection for fertility (that is, for a set of correlated quantitative traits determined by both multiple loci and the environment) leads to an increase in R(L). In terms of adaptive dynamics, the maximum R(L) corresponds to the evolutionary stability and, in certain cases, convergent stability of the values for traits. The search for evolutionarily stable values on the background of limited resources for reproduction is a problem of linear programming.

  17. Nonlinear evolution equations

    CERN Document Server

    Uraltseva, N N

    1995-01-01

    This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p

  18. Mathematical modeling and applications in nonlinear dynamics

    CERN Document Server

    Merdan, Hüseyin

    2016-01-01

    The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...

  19. On the complexity of a combined homotopy interior method for convex programming

    Science.gov (United States)

    Yu, Bo; Xu, Qing; Feng, Guochen

    2007-03-01

    In [G.C. Feng, Z.H. Lin, B. Yu, Existence of an interior pathway to a Karush-Kuhn-Tucker point of a nonconvex programming problem, Nonlinear Anal. 32 (1998) 761-768; G.C. Feng, B. Yu, Combined homotopy interior point method for nonlinear programming problems, in: H. Fujita, M. Yamaguti (Eds.), Advances in Numerical Mathematics, Proceedings of the Second Japan-China Seminar on Numerical Mathematics, Lecture Notes in Numerical and Applied Analysis, vol. 14, Kinokuniya, Tokyo, 1995, pp. 9-16; Z.H. Lin, B. Yu, G.C. Feng, A combined homotopy interior point method for convex programming problem, Appl. Math. Comput. 84 (1997) 193-211.], a combined homotopy was constructed for solving non-convex programming and convex programming with weaker conditions, without assuming the logarithmic barrier function to be strictly convex and the solution set to be bounded. It was proven that a smooth interior path from an interior point of the feasible set to a K-K-T point of the problem exists. This shows that combined homotopy interior point methods can solve the problem that commonly used interior point methods cannot solveE However, so far, there is no result on its complexity, even for linear programming. The main difficulty is that the objective function is not monotonically decreasing on the combined homotopy path. In this paper, by taking a piecewise technique, under commonly used conditions, polynomiality of a combined homotopy interior point method is given for convex nonlinear programming.

  20. Nonlinear finite element analysis of reinforced and prestressed concrete shells with edge beams

    International Nuclear Information System (INIS)

    Srinivasa Rao, P.; Duraiswamy, S.

    1994-01-01

    The structural design of reinforced and prestressed concrete shells demands the application of nonlinear finite element analysis (NFEM) procedures to ensure safety and serviceability. In this paper the details of a comprehensive NFEM program developed are presented. The application of the program is highlighted by solving two numerical problems and comparing the results with experimental results. (author). 20 refs., 15 figs

  1. A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions.

    Science.gov (United States)

    Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin

    2016-01-01

    This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.

  2. A Dynamic Programming Algorithm for the k-Haplotyping Problem

    Institute of Scientific and Technical Information of China (English)

    Zhen-ping Li; Ling-yun Wu; Yu-ying Zhao; Xiang-sun Zhang

    2006-01-01

    The Minimum Fragments Removal (MFR) problem is one of the haplotyping problems: given a set of fragments, remove the minimum number of fragments so that the resulting fragments can be partitioned into k classes of non-conflicting subsets. In this paper, we formulate the k-MFR problem as an integer linear programming problem, and develop a dynamic programming approach to solve the k-MFR problem for both the gapless and gap cases.

  3. Value Iteration Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems.

    Science.gov (United States)

    Wei, Qinglai; Liu, Derong; Lin, Hanquan

    2016-03-01

    In this paper, a value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon undiscounted optimal control problems for discrete-time nonlinear systems. The present value iteration ADP algorithm permits an arbitrary positive semi-definite function to initialize the algorithm. A novel convergence analysis is developed to guarantee that the iterative value function converges to the optimal performance index function. Initialized by different initial functions, it is proven that the iterative value function will be monotonically nonincreasing, monotonically nondecreasing, or nonmonotonic and will converge to the optimum. In this paper, for the first time, the admissibility properties of the iterative control laws are developed for value iteration algorithms. It is emphasized that new termination criteria are established to guarantee the effectiveness of the iterative control laws. Neural networks are used to approximate the iterative value function and compute the iterative control law, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.

  4. One-dimensional singular problems involving the p-Laplacian and nonlinearities indefinite in sign

    OpenAIRE

    Kaufmann, Uriel; Medri, Iván

    2015-01-01

    Let $\\Omega$ be a bounded open interval, let $p>1$ and $\\gamma>0$, and let $m:\\Omega\\rightarrow\\mathbb{R}$ be a function that may change sign in $\\Omega $. In this article we study the existence and nonexistence of positive solutions for one-dimensional singular problems of the form $-(\\left\\vert u^{\\prime}\\right\\vert ^{p-2}u^{\\prime})^{\\prime}=m\\left( x\\right) u^{-\\gamma}$ in $\\Omega$, $u=0$ on $\\partial\\Omega$. As a consequence we also derive existence results for other related nonlinearities.

  5. An Approach for Solving Linear Fractional Programming Problems

    OpenAIRE

    Andrew Oyakhobo Odior

    2012-01-01

    Linear fractional programming problems are useful tools in production planning, financial and corporate planning, health care and hospital planning and as such have attracted considerable research interest. The paper presents a new approach for solving a fractional linear programming problem in which the objective function is a linear fractional function, while the constraint functions are in the form of linear inequalities. The approach adopted is based mainly upon solving the problem algebr...

  6. An Improvement for Fuzzy Stochastic Goal Programming Problems

    Directory of Open Access Journals (Sweden)

    Shu-Cheng Lin

    2017-01-01

    Full Text Available We examined the solution process for linear programming problems under a fuzzy and random environment to transform fuzzy stochastic goal programming problems into standard linear programming problems. A previous paper that revised the solution process with the lower-side attainment index motivated our work. In this paper, we worked on a revision for both-side attainment index to amend its definition and theorems. Two previous examples were used to examine and demonstrate our improvement over previous results. Our findings not only improve the previous paper with both-side attainment index, but also provide a theoretical extension from lower-side attainment index to the both-side attainment index.

  7. Non-linear nuclear engineering models as genetic programming application

    International Nuclear Information System (INIS)

    Domingos, Roberto P.; Schirru, Roberto; Martinez, Aquilino S.

    1997-01-01

    This work presents a Genetic Programming paradigm and a nuclear application. A field of Artificial Intelligence, based on the concepts of Species Evolution and Natural Selection, can be understood as a self-programming process where the computer is the main agent responsible for the discovery of a program able to solve a given problem. In the present case, the problem was to find a mathematical expression in symbolic form, able to express the existent relation between equivalent ratio of a fuel cell, the enrichment of fuel elements and the multiplication factor. Such expression would avoid repeatedly reactor physics codes execution for core optimization. The results were compared with those obtained by different techniques such as Neural Networks and Linear Multiple Regression. Genetic Programming has shown to present a performance as good as, and under some features superior to Neural Network and Linear Multiple Regression. (author). 10 refs., 8 figs., 1 tabs

  8. Bivium as a Mixed Integer Programming Problem

    DEFF Research Database (Denmark)

    Borghoff, Julia; Knudsen, Lars Ramkilde; Stolpe, Mathias

    2009-01-01

    over $GF(2)$ into a combinatorial optimization problem. We convert the Boolean equation system into an equation system over $\\mathbb{R}$ and formulate the problem of finding a $0$-$1$-valued solution for the system as a mixed-integer programming problem. This enables us to make use of several...

  9. ACCULIB, Program Library of Mathematical Routines

    International Nuclear Information System (INIS)

    Van Kats, J.M.; Rusman, C.J.; Van der Vorst, H.A.

    1987-01-01

    Description of program or function - ACCULIB is a collection of programs and subprograms for: - approximation and interpolation problems; - the evaluation of series of orthogonal polynomials; - evaluation of the complementary error function; - sorting problems and permutations; - differential equation problems; - linear algebra eigenvalue problems; - optimization problems; - fast Fourier transformations and Fourier series; - numerical quadrature of continuous functions; - linear systems and other linear algebra problems; - bit manipulation and character handling/transmission; - systems of nonlinear equations, in particular the determination of zeros of polynomials; - solution of over-complete systems; - plotting routines for contouring and surface representation; - statistical investigation of data. In addition, many utilities such as code conversion, microfiche production, disk file surveys, layout improvements for ALGOL60 and FORTRAN programs, and the conversion of IBM FORTRAN programs to CDC FORTRAN are included in the collection

  10. Initial-Boundary Value Problem Solution of the Nonlinear Shallow-water Wave Equations

    Science.gov (United States)

    Kanoglu, U.; Aydin, B.

    2014-12-01

    The hodograph transformation solutions of the one-dimensional nonlinear shallow-water wave (NSW) equations are usually obtained through integral transform techniques such as Fourier-Bessel transforms. However, the original formulation of Carrier and Greenspan (1958 J Fluid Mech) and its variant Carrier et al. (2003 J Fluid Mech) involve evaluation integrals. Since elliptic integrals are highly singular as discussed in Carrier et al. (2003), this solution methodology requires either approximation of the associated integrands by smooth functions or selection of regular initial/boundary data. It should be noted that Kanoglu (2004 J Fluid Mech) partly resolves this issue by simplifying the resulting integrals in closed form. Here, the hodograph transform approach is coupled with the classical eigenfunction expansion method rather than integral transform techniques and a new analytical model for nonlinear long wave propagation over a plane beach is derived. This approach is based on the solution methodology used in Aydın & Kanoglu (2007 CMES-Comp Model Eng) for wind set-down relaxation problem. In contrast to classical initial- or boundary-value problem solutions, here, the NSW equations are formulated to yield an initial-boundary value problem (IBVP) solution. In general, initial wave profile with nonzero initial velocity distribution is assumed and the flow variables are given in the form of Fourier-Bessel series. The results reveal that the developed method allows accurate estimation of the spatial and temporal variation of the flow quantities, i.e., free-surface height and depth-averaged velocity, with much less computational effort compared to the integral transform techniques such as Carrier et al. (2003), Kanoglu (2004), Tinti & Tonini (2005 J Fluid Mech), and Kanoglu & Synolakis (2006 Phys Rev Lett). Acknowledgments: This work is funded by project ASTARTE- Assessment, STrategy And Risk Reduction for Tsunamis in Europe. Grant 603839, 7th FP (ENV.2013.6.4-3 ENV

  11. Model-based problem solving through symbolic regression via pareto genetic programming

    NARCIS (Netherlands)

    Vladislavleva, E.

    2008-01-01

    Pareto genetic programming methodology is extended by additional generic model selection and generation strategies that (1) drive the modeling engine to creation of models of reduced non-linearity and increased generalization capabilities, and (2) improve the effectiveness of the search for robust

  12. Exact Solution of a Faraday's Law Problem that Includes a Nonlinear Term and Its Implication for Perturbation Theory.

    Science.gov (United States)

    Fulcher, Lewis P.

    1979-01-01

    Presents an exact solution to the nonlinear Faraday's law problem of a rod sliding on frictionless rails with resistance. Compares the results with perturbation calculations based on the methods of Poisson and Pincare and of Kryloff and Bogoliuboff. (Author/GA)

  13. FRF decoupling of nonlinear systems

    Science.gov (United States)

    Kalaycıoğlu, Taner; Özgüven, H. Nevzat

    2018-03-01

    Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and led to several decoupling methods. In spite of the inherent nonlinearities in a structural system in various forms such as clearances, friction and nonlinear stiffness, all decoupling studies are for linear systems. In this study, decoupling problem for nonlinear systems is addressed for the first time. A method, named as FRF Decoupling Method for Nonlinear Systems (FDM-NS), is proposed for calculating FRFs of a substructure decoupled from a coupled nonlinear structure where nonlinearity can be modeled as a single nonlinear element. Depending on where nonlinear element is, i.e., either in the known or unknown subsystem, or at the connection point, the formulation differs. The method requires relative displacement information between two end points of the nonlinear element, in addition to point and transfer FRFs at some points of the known subsystem. However, it is not necessary to excite the system from the unknown subsystem even when the nonlinear element is in that subsystem. The validation of FDM-NS is demonstrated with two different case studies using nonlinear lumped parameter systems. Finally, a nonlinear experimental test structure is used in order to show the real-life application and accuracy of FDM-NS.

  14. Existence of Positive Solutions to a Singular Semipositone Boundary Value Problem of Nonlinear Fractional Differential Systems

    Directory of Open Access Journals (Sweden)

    Xiaofeng Zhang

    2017-12-01

    Full Text Available In this paper, we consider the existence of positive solutions to a singular semipositone boundary value problem of nonlinear fractional differential equations. By applying the fixed point index theorem, some new results for the existence of positive solutions are obtained. In addition, an example is presented to demonstrate the application of our main results.

  15. One Layer Nonlinear Economic Closed-Loop Generalized Predictive Control for a Wastewater Treatment Plant

    Directory of Open Access Journals (Sweden)

    Hicham El bahja

    2018-04-01

    Full Text Available The main scope of this paper is the proposal of a new single layer Nonlinear Economic Closed-Loop Generalized Predictive Control (NECLGPC as an efficient advanced control technique for improving economics in the operation of nonlinear plants. Instead of the classic dual-mode MPC (model predictive controller schemes, where the terminal control law defined in the terminal region is obtained offline solving a linear quadratic regulator problem, here the terminal control law in the NECLGPC is determined online by an unconstrained Nonlinear Generalized Predictive Control (NGPC. In order to make the optimization problem more tractable two considerations have been made in the present work. Firstly, the prediction model consisting of a nonlinear phenomenological model of the plant is expressed with linear structure and state dependent matrices. Secondly, instead of including the nonlinear economic cost in the objective function, an approximation of the reduced gradient of the economic function is used. These assumptions allow us to design an economic unconstrained nonlinear GPC analytically and to state the NECLGPC allow for the design of an economic problem as a QP (Quadratic Programing problem each sampling time. Four controllers based on GPC that differ in designs and structures are compared with the proposed control technique in terms of process performance and energy costs. Particularly, the methodology is implemented in the N-Removal process of a Wastewater Treatment Plant (WWTP and the results prove the efficiency of the method and that it can be used profitably in practical cases.

  16. Nonlinear Dynamic Phenomena in Mechanics

    CERN Document Server

    Warminski, Jerzy; Cartmell, Matthew P

    2012-01-01

    Nonlinear phenomena should play a crucial role in the design and control of engineering systems and structures as they can drastically change the prevailing dynamical responses. This book covers theoretical and applications-based problems of nonlinear dynamics concerned with both discrete and continuous systems of interest in civil and mechanical engineering. They include pendulum-like systems, slender footbridges, shape memory alloys, sagged elastic cables and non-smooth problems. Pendulums can be used as a dynamic absorber mounted in high buildings, bridges or chimneys. Geometrical nonlinear

  17. Nonlinear problems in data-assimilation : Can synchronization help?

    Science.gov (United States)

    Tribbia, J. J.; Duane, G. S.

    2009-12-01

    Over the past several years, operational weather centers have initiated ensemble prediction and assimilation techniques to estimate the error covariance of forecasts in the short and the medium range. The ensemble techniques used are based on linear methods. The theory This technique s been shown to be a useful indicator of skill in the linear range where forecast errors are small relative to climatological variance. While this advance has been impressive, there are still ad hoc aspects of its use in practice, like the need for covariance inflation which are troubling. Furthermore, to be of utility in the nonlinear range an ensemble assimilation and prediction method must be capable of giving probabilistic information for the situation where a probability density forecast becomes multi-modal. A prototypical, simplest example of such a situation is the planetary-wave regime transition where the pdf is bimodal. Our recent research show how the inconsistencies and extensions of linear methodology can be consistently treated using the paradigm of synchronization which views the problems of assimilation and forecasting as that of optimizing the forecast model state with respect to the future evolution of the atmosphere.

  18. Nonlinear Boltzmann equation for the homogeneous isotropic case: Minimal deterministic Matlab program

    Science.gov (United States)

    Asinari, Pietro

    2010-10-01

    .gz Programming language: Tested with Matlab version ⩽6.5. However, in principle, any recent version of Matlab or Octave should work Computer: All supporting Matlab or Octave Operating system: All supporting Matlab or Octave RAM: 300 MBytes Classification: 23 Nature of problem: The problem consists in integrating the homogeneous Boltzmann equation for a generic collisional kernel in case of isotropic symmetry, by a deterministic direct method. Difficulties arise from the multi-dimensionality of the collisional operator and from satisfying the conservation of particle number and energy (momentum is trivial for this test case) as accurately as possible, in order to preserve the late dynamics. Solution method: The solution is based on the method proposed by Aristov (2001) [1], but with two substantial improvements: (a) the original problem is reformulated in terms of particle kinetic energy (this allows one to ensure exact particle number and energy conservation during microscopic collisions) and (b) a DVM-like correction (where DVM stands for Discrete Velocity Model) is adopted for improving the relaxation rates (this allows one to satisfy exactly the conservation laws at macroscopic level, which is particularly important for describing the late dynamics in the relaxation towards the equilibrium). Both these corrections make possible to derive very accurate reference solutions for this test case. Restrictions: The nonlinear Boltzmann equation is extremely challenging from the computational point of view, in particular for deterministic methods, despite the increased computational power of recent hardware. In this work, only the homogeneous isotropic case is considered, for making possible the development of a minimal program (by a simple scripting language) and allowing the user to check the advantages of the proposed improvements beyond Aristov's (2001) method [1]. The initial conditions are supposed parameterized according to a fixed analytical expression, but this can be

  19. Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities

    Directory of Open Access Journals (Sweden)

    Y. N. Pavlov

    2015-01-01

    Full Text Available The subject of this work is the problem of identification of nonlinear dynamic systems based on the experimental data obtained by applying test signals to the system. The goal is to determinate coefficients of differential equations of systems by experimental frequency hodographs and separate similar, but different, in essence, forces: dissipative forces with the square of the first derivative in the motion equations and dissipative force from the action of dry friction. There was a proposal to use the harmonic linearization method to approximate each of the nonlinearity of "quadratic friction" and "dry friction" by linear friction with the appropriate harmonic linearization coefficient.Assume that a frequency transfer function of the identified system has a known form. Assume as well that there are disturbances while obtaining frequency characteristics of the realworld system. As a result, the points of experimentally obtained hodograph move randomly. Searching for solution of the identification problem was in the hodograph class, specified by the system model, which has the form of the frequency transfer function the same as the form of the frequency transfer function of the system identified. Minimizing a proximity criterion (measure of the experimentally obtained system hodograph and the system hodograph model for all the experimental points described and previously published by one of the authors allowed searching for the unknown coefficients of the frequenc ransfer function of the system model. The paper shows the possibility to identify a nonlinear dynamic system with multiple nonlinearities, obtained on the experimental samples of the frequency system hodograph. The proposed algorithm allows to select the nonlinearity of the type "quadratic friction" and "dry friction", i.e. also in the case where the nonlinearity is dependent on the same dynamic parameter, in particular, on the derivative of the system output value. For the dynamic

  20. Adaptive Critic Nonlinear Robust Control: A Survey.

    Science.gov (United States)

    Wang, Ding; He, Haibo; Liu, Derong

    2017-10-01

    Adaptive dynamic programming (ADP) and reinforcement learning are quite relevant to each other when performing intelligent optimization. They are both regarded as promising methods involving important components of evaluation and improvement, at the background of information technology, such as artificial intelligence, big data, and deep learning. Although great progresses have been achieved and surveyed when addressing nonlinear optimal control problems, the research on robustness of ADP-based control strategies under uncertain environment has not been fully summarized. Hence, this survey reviews the recent main results of adaptive-critic-based robust control design of continuous-time nonlinear systems. The ADP-based nonlinear optimal regulation is reviewed, followed by robust stabilization of nonlinear systems with matched uncertainties, guaranteed cost control design of unmatched plants, and decentralized stabilization of interconnected systems. Additionally, further comprehensive discussions are presented, including event-based robust control design, improvement of the critic learning rule, nonlinear H ∞ control design, and several notes on future perspectives. By applying the ADP-based optimal and robust control methods to a practical power system and an overhead crane plant, two typical examples are provided to verify the effectiveness of theoretical results. Overall, this survey is beneficial to promote the development of adaptive critic control methods with robustness guarantee and the construction of higher level intelligent systems.

  1. Employee assistance program treats personal problems.

    Science.gov (United States)

    Bednarek, R J; Featherston, H J

    1984-03-01

    Though the concept of employee assistance programs (EAPs) is widely accepted throughout business and industry, few hospitals have established similar channels for dealing with workers whose personal problems cause work-related problems. Among the reasons for the health care profession's lack of involvement in this area are: lack of information about costs and benefits of EAPs; the hospital's multidisciplinary environment in which standards of employee competence and behavior are set by persons from many disciplines; hospital working hours; and health care workers' attitudes about their vulnerability to illness. St. Benedict's Hospital, Ogden, UT, however, has confronted the question of how to demonstrate Christian concern for its employees. St. Benedict's EAP, the Helping Hand, which was created in 1979, combines progressive disciplinary action with the opportunity for early intervention in and treatment of employees' personal problems. When a worker with personal problems is referred to the EAP coordinator, he or she is matched with the appropriate community or hospital resource for treatment. Supervisors are trained to identify employee problems and to focus on employee job performance rather than on attempting to diagnose the problem. St. Benedict's records during the program's first three years illustrate the human benefits as well as the cost savings of an EAP. Of 92 hospital employees who took part in the EAP, 72 improved their situations or resolved their problems. The hospital's turnover rates declined from 36 percent to 20 percent, and approximately $40,800 in turnover and replacement costs were saved.

  2. Variational problems arising in classical mechanics and nonlinear elasticity

    International Nuclear Information System (INIS)

    Spencer, P.

    1999-01-01

    In this thesis we consider two different classes of variational problems. First, one-dimensional problems arising from classical mechanics where the problem is to determine whether there is a unique function η 0 (x) which minimises the energy functional of the form I(η) = ∫ a b L(x,η(x), η'(x)) dx. We will investigate uniqueness by making a change of dependent and independent variables and showing that for a class of integrands L with a particular kind of scaling invariance the resulting integrand is completely convex. The change of variables arises by applying results from Lie group theory as applied in the study of differential equations and this work is motivated by [60] and [68]. Second, the problem of minimising energy functionals of the form E(u) = ∫ A W(∇u(x)) dx in the case of a nonlinear elastic body occupying an annular region A contains R 2 with u : A-bar → A-bar. This work is motivated by [57] (in particular the example of paragraph 4). We will consider rotationally symmetric deformations satisfying prescribed boundary conditions. We will show the existence of minimisers for stored energy functions of the form W(F) = g-tilde(vertical bar-F-vertical bar, det(F)) in a class of general rotationally symmetric deformations of a compressible annulus and for stored energy functions of the form W(F) = g-bar(vertical bar-F-vertical bar) in a class of rotationally symmetric deformations of an incompressible annulus. We will also show that in each case the minimisers are solutions of the full equilibrium equations. A model problem will be considered where the energy functional is the Dirichlet integral and it will be shown that the rotationally symmetric solution obtained is a minimiser among admissible non-rotationally symmetric deformations. In the case of an incompressible annulus, we will consider the Dirichlet integral as the energy functional and show that the rotationally symmetric equilibrium solutions in this case are weak local minimisers in

  3. Mathematical problems in non-linear Physics: some results

    International Nuclear Information System (INIS)

    1979-01-01

    The basic results presented in this report are the following: 1) Characterization of the range and Kernel of the variational derivative. 2) Determination of general conservation laws in linear evolution equations, as well as bounds for the number of polynomial conserved densities in non-linear evolution equations in two independent variables of even order. 3) Construction of the most general evolution equation which has a given family of conserved densities. 4) Regularity conditions for the validity of the Lie invariance method. 5) A simple class of perturbations in non-linear wave equations. 6) Soliton solutions in generalized KdV equations. (author)

  4. Optimization Formulations for the Maximum Nonlinear Buckling Load of Composite Structures

    DEFF Research Database (Denmark)

    Lindgaard, Esben; Lund, Erik

    2011-01-01

    This paper focuses on criterion functions for gradient based optimization of the buckling load of laminated composite structures considering different types of buckling behaviour. A local criterion is developed, and is, together with a range of local and global criterion functions from literature......, benchmarked on a number of numerical examples of laminated composite structures for the maximization of the buckling load considering fiber angle design variables. The optimization formulations are based on either linear or geometrically nonlinear analysis and formulated as mathematical programming problems...... solved using gradient based techniques. The developed local criterion is formulated such it captures nonlinear effects upon loading and proves useful for both analysis purposes and as a criterion for use in nonlinear buckling optimization. © 2010 Springer-Verlag....

  5. H∞ Balancing for Nonlinear Systems

    NARCIS (Netherlands)

    Scherpen, Jacquelien M.A.

    1996-01-01

    In previously obtained balancing methods for nonlinear systems a past and a future energy function are used to bring the nonlinear system in balanced form. By considering a different pair of past and future energy functions that are related to the H∞ control problem for nonlinear systems we define

  6. EZLP: An Interactive Computer Program for Solving Linear Programming Problems. Final Report.

    Science.gov (United States)

    Jarvis, John J.; And Others

    Designed for student use in solving linear programming problems, the interactive computer program described (EZLP) permits the student to input the linear programming model in exactly the same manner in which it would be written on paper. This report includes a brief review of the development of EZLP; narrative descriptions of program features,…

  7. A HIGH ORDER SOLUTION OF THREE DIMENSIONAL TIME DEPENDENT NONLINEAR CONVECTIVE-DIFFUSIVE PROBLEM USING MODIFIED VARIATIONAL ITERATION METHOD

    Directory of Open Access Journals (Sweden)

    Pratibha Joshi

    2014-12-01

    Full Text Available In this paper, we have achieved high order solution of a three dimensional nonlinear diffusive-convective problem using modified variational iteration method. The efficiency of this approach has been shown by solving two examples. All computational work has been performed in MATHEMATICA.

  8. Limits to Nonlinear Inversion

    DEFF Research Database (Denmark)

    Mosegaard, Klaus

    2012-01-01

    For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on our......-heuristics are inefficient for large-scale, non-linear inverse problems, and that the 'no-free-lunch' theorem holds. We discuss typical objections to the relevance of this theorem. A consequence of the no-free-lunch theorem is that algorithms adapted to the mathematical structure of the problem perform more efficiently than...... pure meta-heuristics. We study problem-adapted inversion algorithms that exploit the knowledge of the smoothness of the misfit function of the problem. Optimal sampling strategies exist for such problems, but many of these problems remain hard. © 2012 Springer-Verlag....

  9. Implementation of a multi-layer perception for a non-linear control problem

    International Nuclear Information System (INIS)

    Lister, J.B.; Schnurrenberger, H.; Marmillod, P.

    1990-12-01

    We present the practical application of a 1-hidden-layer multilayer perception (MLP) to provide a non-linear continuous multi-variable mapping with 42 inputs and 13 outputs. The problem resolved is one of extracting information from experimental signals with a bandwidth of many kilohertz. We have an exact model of the inverse mapping of this problem, but we have no explicit form of the required forward mapping. This is the typical situation in data interpretation. The MLP was trained to provide this mapping by learning on 500 input-output examples. The success of the off-line solution to this problem using an MLP led us to examine the robustness of the MLP to different noise sources. We found that the MLP is more robust than an approximate linear mapping of the same problem. 12 bits of resolution in the weights are necessary to avoid a significant loss of precision. The practical implementation of large analog weight matrices using DAS-multipliers and a simple segmented sigmoid is also presented. A General Adaptive Recipe (GAR) for improving the performance of conventional back-propagation was developed. The GAR uses an adaptive step length and both the bias terms and the initial weight seeding are determined by the network size. The GAR was found to be robust and much faster than conventional back-propagation. (author) 20 figs., 1 tab., 15 refs

  10. Snap-Through Buckling Problem of Spherical Shell Structure

    Directory of Open Access Journals (Sweden)

    Sumirin Sumirin

    2014-12-01

    Full Text Available This paper presents results of a numerical study on the nonlinear behavior of shells undergoing snap-through instability. This research investigates the problem of snap-through buckling of spherical shells applying nonlinear finite element analysis utilizing ANSYS Program. The shell structure was modeled by axisymmetric thin shell of finite elements. Shells undergoing snap-through buckling meet with significant geometric change of their physical configuration, i.e. enduring large deflections during their deformation process. Therefore snap-through buckling of shells basically is a nonlinear problem. Nonlinear numerical operations need to be applied in their analysis. The problem was solved by a scheme of incremental iterative procedures applying Newton-Raphson method in combination with the known line search as well as the arc- length methods. The effects of thickness and depth variation of the shell is taken care of by considering their geometrical parameter l. The results of this study reveal that spherical shell structures subjected to pressure loading experience snap-through instability for values of l≥2.15. A form of ‘turn-back’ of the load-displacement curve took place at load levels prior to the achievement of the critical point. This phenomenon was observed for values of l=5.0 to l=7.0.

  11. SOCP relaxation bounds for the optimal subset selection problem applied to robust linear regression

    OpenAIRE

    Flores, Salvador

    2015-01-01

    This paper deals with the problem of finding the globally optimal subset of h elements from a larger set of n elements in d space dimensions so as to minimize a quadratic criterion, with an special emphasis on applications to computing the Least Trimmed Squares Estimator (LTSE) for robust regression. The computation of the LTSE is a challenging subset selection problem involving a nonlinear program with continuous and binary variables, linked in a highly nonlinear fashion. The selection of a ...

  12. Global solutions to the initial-boundary value problem for the quasilinear viscoelastic equation with a derivative nonlinearity

    Directory of Open Access Journals (Sweden)

    Mitsuhiro Nakao

    2014-01-01

    Full Text Available We prove the existence and uniqueness of a global decaying solution to the initial boundary value problem for the quasilinear wave equation with Kelvin-Voigt dissipation and a derivative nonlinearity. To derive the required estimates of the solutions we employ a 'loan' method and use a difference inequality on the energy.

  13. New results on the mathematical problems in nonlinear physics

    International Nuclear Information System (INIS)

    1980-01-01

    The main topics treated in this report are: I) Existence of generalized Lagrangians. II) Conserved densities for odd-order polynomial evolution equations and linear evolution systems. III ) Conservation laws for Klein-Gordon, Di rae and Maxwell equations. IV) Stability conditions for finite-energy solutions of a non-linear Klein-Gordon equation. V) Hamiltonian approach to non-linear evolution equations and Backlund transformations. VI) Anharmonic vibrations: Status of results and new possible approaches. (Author) 83 refs

  14. PENNON: A code for convex nonlinear and semidefinite programming

    Czech Academy of Sciences Publication Activity Database

    Kočvara, Michal; Stingl, M.

    2003-01-01

    Roč. 18, č. 3 (2003), s. 317-333 ISSN 1055-6788 R&D Projects: GA ČR GA201/00/0080 Grant - others:BMBF(DE) 03ZOM3ER Institutional research plan: CEZ:AV0Z1075907 Keywords : convex programming * semidefinite programming * large-scale problems Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.306, year: 2003

  15. Problem of two-level hierarchical minimax program control the final state of regional social and economic system in the presence of risks

    International Nuclear Information System (INIS)

    Shorikov, A. F.

    2015-01-01

    This article discusses a discrete-time dynamical system consisting of a set a controllable objects (region and forming it municipalities). The dynamics each of these is described by the corresponding vector nonlinear discrete-time recurrent vector equations and its control system consist from two levels: basic (control level I) that is dominating and subordinate level (control level II). Both levels have different criterions of functioning and united a priori by determined informational and control connections defined in advance. In this paper we study the problem of optimization of guaranteed result for program control by the final state of regional social and economic system in the presence of risks. For this problem we proposed in this work an economical and mathematical model of two-level hierarchical minimax program control the final state of regional social and economic system in the presence of risks and the general scheme for its solving

  16. Problem of two-level hierarchical minimax program control the final state of regional social and economic system in the presence of risks

    Energy Technology Data Exchange (ETDEWEB)

    Shorikov, A. F., E-mail: afshorikov@mail.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002, Russia Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990 (Russian Federation)

    2015-11-30

    This article discusses a discrete-time dynamical system consisting of a set a controllable objects (region and forming it municipalities). The dynamics each of these is described by the corresponding vector nonlinear discrete-time recurrent vector equations and its control system consist from two levels: basic (control level I) that is dominating and subordinate level (control level II). Both levels have different criterions of functioning and united a priori by determined informational and control connections defined in advance. In this paper we study the problem of optimization of guaranteed result for program control by the final state of regional social and economic system in the presence of risks. For this problem we proposed in this work an economical and mathematical model of two-level hierarchical minimax program control the final state of regional social and economic system in the presence of risks and the general scheme for its solving.

  17. Averaging of nonlinearity-managed pulses

    International Nuclear Information System (INIS)

    Zharnitsky, Vadim; Pelinovsky, Dmitry

    2005-01-01

    We consider the nonlinear Schroedinger equation with the nonlinearity management which describes Bose-Einstein condensates under Feshbach resonance. By using an averaging theory, we derive the Hamiltonian averaged equation and compare it with other averaging methods developed for this problem. The averaged equation is used for analytical approximations of nonlinearity-managed solitons

  18. A Generalized National Planning Approach for Admission Capacity in Higher Education: A Nonlinear Integer Goal Programming Model with a Novel Differential Evolution Algorithm.

    Science.gov (United States)

    El-Qulity, Said Ali; Mohamed, Ali Wagdy

    2016-01-01

    This paper proposes a nonlinear integer goal programming model (NIGPM) for solving the general problem of admission capacity planning in a country as a whole. The work aims to satisfy most of the required key objectives of a country related to the enrollment problem for higher education. The system general outlines are developed along with the solution methodology for application to the time horizon in a given plan. The up-to-date data for Saudi Arabia is used as a case study and a novel evolutionary algorithm based on modified differential evolution (DE) algorithm is used to solve the complexity of the NIGPM generated for different goal priorities. The experimental results presented in this paper show their effectiveness in solving the admission capacity for higher education in terms of final solution quality and robustness.

  19. Degenerate nonlinear diffusion equations

    CERN Document Server

    Favini, Angelo

    2012-01-01

    The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...

  20. Adolescent Assertiveness: Problems and Programs.

    Science.gov (United States)

    Reece, Randi S.; Wilborn, Bobbie L.

    1980-01-01

    Assertiveness training programs in the school setting provide a method to work with students with behavior problems. When students can manage their environments more effectively, they view the educational experience more positively and find that their present world and their transition to the adult world proceeds more productively. (Author)

  1. Near-field soil-structure interaction analysis using nonlinear hybrid modeling

    International Nuclear Information System (INIS)

    Katayama, I.; Chen, C.; Lee, Y.J.; Jean, W.Y.; Penzien, J.

    1989-01-01

    The hybrid modeling method (Gupta and Penzien 1980) and associated analysis procedure for solving a three-dimensional soil-structure interaction problem was developed by Gupta and Penzien (1981) and Gupta et al.(1982). Subsequently, successive modifications have been made to the original modeling method and analysis procedure allowing more general treatment of the SSI problem (Penzien, 1988). Through many correlation studies of field test data obtained under forced-vibration and earthquake-excitation conditions, it has been shown that the HASSI programs can effectively predict the dynamic response of a soil-structure system, if realistic soil parameters are adopted. In the above, the entire structure-foundation system is considered to respond in a linear fashion. Since the reflected three-dimensional waves at the soil-structure interface decays very rapidly with distance away from the structure (Katayama, 1987 (a)), the response of the soil close to the base of the structure may greatly affect its response; therefore, proper modeling of the non-linear soil behavior characteristic is essential. The nonlinear behavior of near-field soil has been taken into consideration in HASSI-7 by the standard equivalent linearization procedures used in programs SHAKE and FLUSH

  2. Technical program to study the benefits of nonlinear analysis methods in LWR component designs. Technical report TR-3723-1

    International Nuclear Information System (INIS)

    Raju, P.P.

    1980-05-01

    This report summarizes the results of the study program to assess the benefits of nonlinear analysis methods in Light Water Reactor (LWR) component designs. The current study reveals that despite its increased cost and other complexities, nonlinear analysis is a practical and valuable tool for the design of LWR components, especially under ASME Level D service conditions (faulted conditions) and it will greatly assist in the evaluation of ductile fracture potential of pressure boundary components. Since the nonlinear behavior is generally a local phenomenon, the design of complex components can be accomplished through substructuring isolated localized regions and evaluating them in detail using nonlinear analysis methods

  3. Convergence rates and finite-dimensional approximations for nonlinear ill-posed problems involving monotone operators in Banach spaces

    International Nuclear Information System (INIS)

    Nguyen Buong.

    1992-11-01

    The purpose of this paper is to investigate convergence rates for an operator version of Tikhonov regularization constructed by dual mapping for nonlinear ill-posed problems involving monotone operators in real reflective Banach spaces. The obtained results are considered in combination with finite-dimensional approximations for the space. An example is considered for illustration. (author). 15 refs

  4. A nonlinear programming approach to lower bounds for the ground-state energy of helium

    International Nuclear Information System (INIS)

    Porras, I.; Feldmann, D.M.; King, F.W.

    1999-01-01

    Lower-bound estimates for the ground-state energy of the helium atom are determined using nonlinear programming techniques. Optimized lower bounds are determined for single-particle, radially correlated, and general correlated wave functions. The local nature of the method employed makes it a very severe test of the accuracy of the wave function

  5. A nonlinear plate control without linearization

    Directory of Open Access Journals (Sweden)

    Yildirim Kenan

    2017-03-01

    Full Text Available In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.

  6. Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review

    Directory of Open Access Journals (Sweden)

    Mahmoud Bayat

    Full Text Available This review features a survey of some recent developments in asymptotic techniques and new developments, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the achieved approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modified perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to over-come the shortcomings.In this review we have applied different powerful analytical methods to solve high nonlinear problems in engineering vibrations. Some patterns are given to illustrate the effectiveness and convenience of the methodologies.

  7. Propeller-Pendulum for Nonlinear UAVs Control

    Directory of Open Access Journals (Sweden)

    Tomáš Huba

    2013-02-01

    Full Text Available This paper presents basic information about new experiment and about the wrapped-around learning objects for nonlinear control and other relevant topics from the mechatronics area. Its primary aim is to motivate students within the framework of the “learning by playing”, “learning by discovering”, or through “experiential learning” approaches to drag them to study this highly sophisticated stuff. The experiment may deal with simple but challenging positional or velocity control tasks requiring knowledge of basic physical principals of mechanics and of the associated mathematical apparatus of nonlinear differential equations. Furthermore, it is also used to master related measurement and communication problems, to carry out embedded control design and programming of embedded devices. Finally, it is also useful and illustrative in comparing traditional control methods that may be confronted towards the latest development in several areas of modern control theory.

  8. Probabilistic dual heuristic programming-based adaptive critic

    Science.gov (United States)

    Herzallah, Randa

    2010-02-01

    Adaptive critic (AC) methods have common roots as generalisations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, non-linear and non-stationary environments. In this study, a novel probabilistic dual heuristic programming (DHP)-based AC controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) AC method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterised by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the probabilistic critic network is then calculated and shown to be equal to the analytically derived correct value. Full derivation of the Riccati solution for this non-standard stochastic linear quadratic control problem is also provided. Moreover, the performance of the proposed probabilistic controller is demonstrated on linear and non-linear control examples.

  9. An overview of adaptive model theory: solving the problems of redundancy, resources, and nonlinear interactions in human movement control.

    Science.gov (United States)

    Neilson, Peter D; Neilson, Megan D

    2005-09-01

    Adaptive model theory (AMT) is a computational theory that addresses the difficult control problem posed by the musculoskeletal system in interaction with the environment. It proposes that the nervous system creates motor maps and task-dependent synergies to solve the problems of redundancy and limited central resources. These lead to the adaptive formation of task-dependent feedback/feedforward controllers able to generate stable, noninteractive control and render nonlinear interactions unobservable in sensory-motor relationships. AMT offers a unified account of how the nervous system might achieve these solutions by forming internal models. This is presented as the design of a simulator consisting of neural adaptive filters based on cerebellar circuitry. It incorporates a new network module that adaptively models (in real time) nonlinear relationships between inputs with changing and uncertain spectral and amplitude probability density functions as is the case for sensory and motor signals.

  10. Numerical nonlinear complex geometrical optics algorithm for the 3D Calderón problem

    DEFF Research Database (Denmark)

    Delbary, Fabrice; Knudsen, Kim

    2014-01-01

    to the generalized Laplace equation. The 3D problem was solved in theory in late 1980s using complex geometrical optics solutions and a scattering transform. Several approximations to the reconstruction method have been suggested and implemented numerically in the literature, but here, for the first time, a complete...... computer implementation of the full nonlinear algorithm is given. First a boundary integral equation is solved by a Nystrom method for the traces of the complex geometrical optics solutions, second the scattering transform is computed and inverted using fast Fourier transform, and finally a boundary value...

  11. The forced nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Kaup, D.J.; Hansen, P.J.

    1985-01-01

    The nonlinear Schroedinger equation describes the behaviour of a radio frequency wave in the ionosphere near the reflexion point where nonlinear processes are important. A simple model of this phenomenon leads to the forced nonlinear Schroedinger equation in terms of a nonlinear boundary value problem. A WKB analysis of the time evolution equations for the nonlinear Schroedinger equation in the inverse scattering transform formalism gives a crude order of magnitude estimation of the qualitative behaviour of the solutions. This estimation is compared with the numerical solutions. (D.Gy.)

  12. Bilevel programming problems theory, algorithms and applications to energy networks

    CERN Document Server

    Dempe, Stephan; Pérez-Valdés, Gerardo A; Kalashnykova, Nataliya; Kalashnikova, Nataliya

    2015-01-01

    This book describes recent theoretical findings relevant to bilevel programming in general, and in mixed-integer bilevel programming in particular. It describes recent applications in energy problems, such as the stochastic bilevel optimization approaches used in the natural gas industry. New algorithms for solving linear and mixed-integer bilevel programming problems are presented and explained.

  13. Relation of deformed nonlinear algebras with linear ones

    International Nuclear Information System (INIS)

    Nowicki, A; Tkachuk, V M

    2014-01-01

    The relation between nonlinear algebras and linear ones is established. For a one-dimensional nonlinear deformed Heisenberg algebra with two operators we find the function of deformation for which this nonlinear algebra can be transformed to a linear one with three operators. We also establish the relation between the Lie algebra of total angular momentum and corresponding nonlinear one. This relation gives a possibility to simplify and to solve the eigenvalue problem for the Hamiltonian in a nonlinear case using the reduction of this problem to the case of linear algebra. It is demonstrated in an example of a harmonic oscillator. (paper)

  14. Inexact nonlinear improved fuzzy chance-constrained programming model for irrigation water management under uncertainty

    Science.gov (United States)

    Zhang, Chenglong; Zhang, Fan; Guo, Shanshan; Liu, Xiao; Guo, Ping

    2018-01-01

    An inexact nonlinear mλ-measure fuzzy chance-constrained programming (INMFCCP) model is developed for irrigation water allocation under uncertainty. Techniques of inexact quadratic programming (IQP), mλ-measure, and fuzzy chance-constrained programming (FCCP) are integrated into a general optimization framework. The INMFCCP model can deal with not only nonlinearities in the objective function, but also uncertainties presented as discrete intervals in the objective function, variables and left-hand side constraints and fuzziness in the right-hand side constraints. Moreover, this model improves upon the conventional fuzzy chance-constrained programming by introducing a linear combination of possibility measure and necessity measure with varying preference parameters. To demonstrate its applicability, the model is then applied to a case study in the middle reaches of Heihe River Basin, northwest China. An interval regression analysis method is used to obtain interval crop water production functions in the whole growth period under uncertainty. Therefore, more flexible solutions can be generated for optimal irrigation water allocation. The variation of results can be examined by giving different confidence levels and preference parameters. Besides, it can reflect interrelationships among system benefits, preference parameters, confidence levels and the corresponding risk levels. Comparison between interval crop water production functions and deterministic ones based on the developed INMFCCP model indicates that the former is capable of reflecting more complexities and uncertainties in practical application. These results can provide more reliable scientific basis for supporting irrigation water management in arid areas.

  15. Inverse atmospheric radiative transfer problems - A nonlinear minimization search method of solution. [aerosol pollution monitoring

    Science.gov (United States)

    Fymat, A. L.

    1976-01-01

    The paper studies the inversion of the radiative transfer equation describing the interaction of electromagnetic radiation with atmospheric aerosols. The interaction can be considered as the propagation in the aerosol medium of two light beams: the direct beam in the line-of-sight attenuated by absorption and scattering, and the diffuse beam arising from scattering into the viewing direction, which propagates more or less in random fashion. The latter beam has single scattering and multiple scattering contributions. In the former case and for single scattering, the problem is reducible to first-kind Fredholm equations, while for multiple scattering it is necessary to invert partial integrodifferential equations. A nonlinear minimization search method, applicable to the solution of both types of problems has been developed, and is applied here to the problem of monitoring aerosol pollution, namely the complex refractive index and size distribution of aerosol particles.

  16. Computer programs for solving systems of nonlinear equations

    International Nuclear Information System (INIS)

    Asaoka, Takumi

    1978-03-01

    Computer programs to find a solution, usually the one closest to some guess, of a system of simultaneous nonlinear equations are provided for real functions of the real arguments. These are based on quasi-Newton methods or projection methods, which are briefly reviewed in the present report. Benchmark tests were performed on these subroutines to grasp their characteristics. As the program not requiring analytical forms of the derivatives of the Jacobian matrix, we have dealt with NS01A of Powell, NS03A of Reid for a system with the sparse Jacobian and NONLIN of Brown. Of these three subroutines of quasi-Newton methods, NONLIN is shown to be the most useful because of its stable algorithm and short computation time. On the other hand, as the subroutine for which the derivatives of the Jacobian are to be supplied analytically, we have tested INTECH of a quasi-Newton method based on the Boggs' algorithm, PROJA of Georg and Keller based on the projection method and an option of NS03A. The results have shown that INTECH, treating variables which appear only linearly in the functions separately, takes the shortest computation time, on the whole, while the projection method requires further research to find an optimal algorithm. (auth.)

  17. Nonlinearity Mechanism and Correction of Sapphire Fiber Temperature Sensor on Blackbody Cavity

    Directory of Open Access Journals (Sweden)

    Tiejun Cao

    2014-06-01

    Full Text Available Based on the principle of blackbody radiation, sapphire optic fiber temperature sensor has been more widely used in recent years, and its temperature range is between 800 ~ 2000 oC, and the response time is in 10-2 magnitude, and transient temperature measurement can be high precision in harsh environments. Nonlinear constraints on sapphire fiber temperature sensor affect the accuracy and stability of the sensor. In order to solve the nonlinear problems which exist in the measurement, at first, the sapphire fiber optic temperature sensor temperature measurement principle and nonlinear generation mechanism are studied; secondly piecewise linear interpolation and spline interpolation linearization algorithm is designed with combining the nonlinear characteristics of sapphire optical fiber temperature sensor, and the program is designed on its linear and associated signal processing. Experimental results show that a good linearization of sapphire fiber optic temperature sensor can been achieved in this method.

  18. Inexact Newton–Landweber iteration for solving nonlinear inverse problems in Banach spaces

    International Nuclear Information System (INIS)

    Jin, Qinian

    2012-01-01

    By making use of duality mappings, we formulate an inexact Newton–Landweber iteration method for solving nonlinear inverse problems in Banach spaces. The method consists of two components: an outer Newton iteration and an inner scheme providing the increments by applying the Landweber iteration in Banach spaces to the local linearized equations. It has the advantage of reducing computational work by computing more cheap steps in each inner scheme. We first prove a convergence result for the exact data case. When the data are given approximately, we terminate the method by a discrepancy principle and obtain a weak convergence result. Finally, we test the method by reporting some numerical simulations concerning the sparsity recovery and the noisy data containing outliers. (paper)

  19. Eigenvalue problem and nonlinear evolution of kink modes in a toroidal plasma

    International Nuclear Information System (INIS)

    Ogino, T.; Takeda, S.; Sanuki, H.; Kamimura, T.

    1979-04-01

    The internal kink modes of a cylindrical plasma are investigated by a linear eigen value problem and their nonlinear evolution is studied by 3-dimensional MHD simulation based on the rectangular column model under the fixed boundary condition. The growth rates in two cases, namely uniform and diffused current profiles are analyzed in detail, which agree with the analytical estimation by Shafranov. The time evolution of the m = 1 mode showed that q > 1 is satisfied at the relaxation time (q safety factor), a stable configuration like a horse shoe (a new equilibrium) was formed. Also, the time evolution of the pressure p for the m = 2 mode showed that a stable configuration like a pair of anchors was formed. (author)

  20. Nonlinear analysis

    CERN Document Server

    Gasinski, Leszek

    2005-01-01

    Hausdorff Measures and Capacity. Lebesgue-Bochner and Sobolev Spaces. Nonlinear Operators and Young Measures. Smooth and Nonsmooth Analysis and Variational Principles. Critical Point Theory. Eigenvalue Problems and Maximum Principles. Fixed Point Theory.

  1. Nonlinear analysis of reinforced concrete structures subjected to high temperature and external load

    International Nuclear Information System (INIS)

    Sugawara, Y.; Goto, M.; Saito, K.; Suzuki, N.; Muto, A.; Ueda, M.

    1993-01-01

    A quarter of a century has passed since the finite element method was first applied to nonlinear problems concerning reinforced concrete structures, and the reliability of the analysis at ordinary temperature has been enhanced accordingly. By contrast, few studies have tried to deal with the nonlinear behavior of reinforced concrete structures subjected to high temperature and external loads simultaneously. It is generally known that the mechanical properties of concrete and steel are affected greatly by temperature. Therefore, in order to analyze the nonlinear behavior of reinforced concrete subjected to external loads at high temperature, it is necessary to construct constitutive models of the materials reflecting the influence of temperature. In this study, constitutive models of concrete and reinforcement that can express decreases in strength and stiffness at high temperature have been developed. A two-dimensional nonlinear finite element analysis program has been developed by use of these material models. The behavior of reinforced concrete beams subjected simultaneously to high temperature and shear forces were simulated using the developed analytical method. The results of the simulation agreed well with the experimental results, evidencing the validity of the developed material models and the finite element analysis program

  2. Optimal control of LQG problem with an explicit trade-off between mean and variance

    Science.gov (United States)

    Qian, Fucai; Xie, Guo; Liu, Ding; Xie, Wenfang

    2011-12-01

    For discrete-time linear-quadratic Gaussian (LQG) control problems, a utility function on the expectation and the variance of the conventional performance index is considered. The utility function is viewed as an overall objective of the system and can perform the optimal trade-off between the mean and the variance of performance index. The nonlinear utility function is first converted into an auxiliary parameters optimisation problem about the expectation and the variance. Then an optimal closed-loop feedback controller for the nonseparable mean-variance minimisation problem is designed by nonlinear mathematical programming. Finally, simulation results are given to verify the algorithm's effectiveness obtained in this article.

  3. Linear decomposition approach for a class of nonconvex programming problems.

    Science.gov (United States)

    Shen, Peiping; Wang, Chunfeng

    2017-01-01

    This paper presents a linear decomposition approach for a class of nonconvex programming problems by dividing the input space into polynomially many grids. It shows that under certain assumptions the original problem can be transformed and decomposed into a polynomial number of equivalent linear programming subproblems. Based on solving a series of liner programming subproblems corresponding to those grid points we can obtain the near-optimal solution of the original problem. Compared to existing results in the literature, the proposed algorithm does not require the assumptions of quasi-concavity and differentiability of the objective function, and it differs significantly giving an interesting approach to solving the problem with a reduced running time.

  4. On Inverse Coefficient Heat-Conduction Problems on Reconstruction of Nonlinear Components of the Thermal-Conductivity Tensor of Anisotropic Bodies

    Science.gov (United States)

    Formalev, V. F.; Kolesnik, S. A.

    2017-11-01

    The authors are the first to present a closed procedure for numerical solution of inverse coefficient problems of heat conduction in anisotropic materials used as heat-shielding ones in rocket and space equipment. The reconstructed components of the thermal-conductivity tensor depend on temperature (are nonlinear). The procedure includes the formation of experimental data, the implicit gradient-descent method, the economical absolutely stable method of numerical solution of parabolic problems containing mixed derivatives, the parametric identification, construction, and numerical solution of the problem for elements of sensitivity matrices, the development of a quadratic residual functional and regularizing functionals, and also the development of algorithms and software systems. The implicit gradient-descent method permits expanding the quadratic functional in a Taylor series with retention of the linear terms for the increments of the sought functions. This substantially improves the exactness and stability of solution of the inverse problems. Software systems are developed with account taken of the errors in experimental data and disregarding them. On the basis of a priori assumptions of the qualitative behavior of the functional dependences of the components of the thermal-conductivity tensor on temperature, regularizing functionals are constructed by means of which one can reconstruct the components of the thermal-conductivity tensor with an error no higher than the error of the experimental data. Results of the numerical solution of the inverse coefficient problems on reconstruction of nonlinear components of the thermal-conductivity tensor have been obtained and are discussed.

  5. Nonlinear Approaches in Engineering Applications

    CERN Document Server

    Jazar, Reza

    2012-01-01

    Nonlinear Approaches in Engineering Applications focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic systems, optimal control and approaches in nonlinear dynamics and acoustics. Coverage encompasses a wide range of applications and fields including mathematical modeling and nonlinear behavior as applied to microresonators, nanotechnologies, nonlinear behavior in soil erosion,nonlinear population dynamics, and optimization in reducing vibration and noise as well as vibration in triple-walled carbon nanotubes. This book also: Provides a complete introduction to nonlinear behavior of systems and the advantages of nonlinearity as a tool for solving engineering problems Includes applications and examples drawn from the el...

  6. Nonlinear dynamics of intense EM pulses in plasma

    International Nuclear Information System (INIS)

    Mahajan, Ranju; Gill, Tarsem Singh; Kaur, Ravinder

    2010-01-01

    The evolution of laser beam in underdense/overdense plasma medium which is key to understanding of several nonlinear processes and underlying physics is governed by nonlinear parabolic equation. The nonlinearity considered here is of relativistic as well as of ponderomotive type. We have set Lagrangian for the problem and reduced Lagrangian problem is solved using appropriate trial function. Equation for the beam width and phase are derived. Further, these equations are used to solve eigenvalue problem for the stability of laser beam evolution and Hurwitz condition is satisfied.

  7. Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

    International Nuclear Information System (INIS)

    Bonnet, M.; Meurant, G.

    1978-01-01

    Different methods of solution of linear and nonlinear algebraic systems are applied to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems, methods in general use of alternating directions type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method on nonlinear conjugate gradient is studied as also Newton's method and some of its variants. It should be noted, however that Newton's method is found to be more efficient when coupled with a good method for solution of the linear system. To conclude, such methods are used to solve a nonlinear diffusion problem and the numerical results obtained are to be compared [fr

  8. Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

    International Nuclear Information System (INIS)

    Bonnet, M.; Meurant, G.

    1978-01-01

    The object of this study is to compare different methods of solving linear and nonlinear algebraic systems and to apply them to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems the conventional methods of alternating direction type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method of nonlinear conjugate gradient is studied together with Newton's method and some of its variants. It should be noted, however, that Newton's method is found to be more efficient when coupled with a good method for solving the linear system. As a conclusion, these methods are used to solve a nonlinear diffusion problem and the numerical results obtained are compared [fr

  9. The cost of uncertainty in capacity expansion problems

    Energy Technology Data Exchange (ETDEWEB)

    Jenhung Wang [National Chung Cheng Univ., Dept. of Business Administration, Chia-Yi (Taiwan); Sparrow, F.T. [Purdue Univ., School of Industrial Engineering, West Lafayette, IN (United States)

    1999-07-01

    The goals of this paper are to present a two-stage programming model of the capacity expansion problem under uncertainty of demand and explore the impact of the uncertainty on cost. The model is a mixed integer nonlinear programming (MINLP) model with the consideration of uncertainty used to maximise the expected presented value of utility profits over the planning horizon, under the constraints of rate of return and reserve margin regulation. The results reveal that the uncertainty harms the profit seriously. In this paper both microeconomics and mathematical programming are used to analyse the problem. We try to observe the economic behaviour of the utility with uncertainty involved. We also investigate the influence on the cost of uncertainty of each economic parameter. (Author)

  10. Flutter analysis of an airfoil with multiple nonlinearities and uncertainties

    Directory of Open Access Journals (Sweden)

    Haitao Liao

    2013-09-01

    Full Text Available An original method for calculating the limit cycle oscillations of nonlinear aero-elastic system is presented. The problem of determining the maximum vibration amplitude of limit cycle is transformed into a nonlinear optimization problem. The harmonic balance method and the Floquet theory are selected to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated and used to analyse the limit cycle oscillations of an airfoil with multiple nonlinearities and uncertainties. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.

  11. NONLINEAR MODEL PREDICTIVE CONTROL OF CHEMICAL PROCESSES

    Directory of Open Access Journals (Sweden)

    SILVA R. G.

    1999-01-01

    Full Text Available A new algorithm for model predictive control is presented. The algorithm utilizes a simultaneous solution and optimization strategy to solve the model's differential equations. The equations are discretized by equidistant collocation, and along with the algebraic model equations are included as constraints in a nonlinear programming (NLP problem. This algorithm is compared with the algorithm that uses orthogonal collocation on finite elements. The equidistant collocation algorithm results in simpler equations, providing a decrease in computation time for the control moves. Simulation results are presented and show a satisfactory performance of this algorithm.

  12. An inertia-free filter line-search algorithm for large-scale nonlinear programming

    Energy Technology Data Exchange (ETDEWEB)

    Chiang, Nai-Yuan; Zavala, Victor M.

    2016-02-15

    We present a filter line-search algorithm that does not require inertia information of the linear system. This feature enables the use of a wide range of linear algebra strategies and libraries, which is essential to tackle large-scale problems on modern computing architectures. The proposed approach performs curvature tests along the search step to detect negative curvature and to trigger convexification. We prove that the approach is globally convergent and we implement the approach within a parallel interior-point framework to solve large-scale and highly nonlinear problems. Our numerical tests demonstrate that the inertia-free approach is as efficient as inertia detection via symmetric indefinite factorizations. We also demonstrate that the inertia-free approach can lead to reductions in solution time because it reduces the amount of convexification needed.

  13. Learning-Based Adaptive Optimal Tracking Control of Strict-Feedback Nonlinear Systems.

    Science.gov (United States)

    Gao, Weinan; Jiang, Zhong-Ping; Weinan Gao; Zhong-Ping Jiang; Gao, Weinan; Jiang, Zhong-Ping

    2018-06-01

    This paper proposes a novel data-driven control approach to address the problem of adaptive optimal tracking for a class of nonlinear systems taking the strict-feedback form. Adaptive dynamic programming (ADP) and nonlinear output regulation theories are integrated for the first time to compute an adaptive near-optimal tracker without any a priori knowledge of the system dynamics. Fundamentally different from adaptive optimal stabilization problems, the solution to a Hamilton-Jacobi-Bellman (HJB) equation, not necessarily a positive definite function, cannot be approximated through the existing iterative methods. This paper proposes a novel policy iteration technique for solving positive semidefinite HJB equations with rigorous convergence analysis. A two-phase data-driven learning method is developed and implemented online by ADP. The efficacy of the proposed adaptive optimal tracking control methodology is demonstrated via a Van der Pol oscillator with time-varying exogenous signals.

  14. A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 3: Design philosophy and programming details

    Science.gov (United States)

    Torak, L.J.

    1993-01-01

    A MODular Finite-Element, digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water-flow. The modular structure of MODFE places the computationally independent tasks that are performed routinely by digital-computer programs simulating ground-water flow into separate subroutines, which are executed from the main program by control statements. Each subroutine consists of complete sets of computations, or modules, which are identified by comment statements, and can be modified by the user without affecting unrelated computations elsewhere in the program. Simulation capabilities can be added or modified by either adding or modifying subroutines that perform specific computational tasks, and the modular-program structure allows the user to create versions of MODFE that contain only the simulation capabilities that pertain to the ground-water problem of interest. MODFE is written in a Fortran programming language that makes it virtually device independent and compatible with desk-top personal computers and large mainframes. MODFE uses computer storage and execution time efficiently by taking advantage of symmetry and sparseness within the coefficient matrices of the finite-element equations. Parts of the matrix coefficients are computed and stored as single-subscripted variables, which are assembled into a complete coefficient just prior to solution. Computer storage is reused during simulation to decrease storage requirements. Descriptions of subroutines that execute the computational steps of the modular-program structure are given in tables that cross reference the subroutines with particular versions of MODFE. Programming details of linear and nonlinear hydrologic terms are provided. Structure diagrams for the main programs show the order in which subroutines are executed for each version and illustrate some of the linear and nonlinear versions of MODFE that are possible. Computational aspects of

  15. Nature Inspired Computational Technique for the Numerical Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology

    Directory of Open Access Journals (Sweden)

    Suheel Abdullah Malik

    2014-01-01

    Full Text Available We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA, interior point algorithm (IPA, and active set algorithm (ASA. The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions.

  16. An efficient method for generalized linear multiplicative programming problem with multiplicative constraints.

    Science.gov (United States)

    Zhao, Yingfeng; Liu, Sanyang

    2016-01-01

    We present a practical branch and bound algorithm for globally solving generalized linear multiplicative programming problem with multiplicative constraints. To solve the problem, a relaxation programming problem which is equivalent to a linear programming is proposed by utilizing a new two-phase relaxation technique. In the algorithm, lower and upper bounds are simultaneously obtained by solving some linear relaxation programming problems. Global convergence has been proved and results of some sample examples and a small random experiment show that the proposed algorithm is feasible and efficient.

  17. Existence of Positive Solutions to a Boundary Value Problem for a Delayed Nonlinear Fractional Differential System

    Directory of Open Access Journals (Sweden)

    Chen Yuming

    2011-01-01

    Full Text Available Though boundary value problems for fractional differential equations have been extensively studied, most of the studies focus on scalar equations and the fractional order between 1 and 2. On the other hand, delay is natural in practical systems. However, not much has been done for fractional differential equations with delays. Therefore, in this paper, we consider a boundary value problem of a general delayed nonlinear fractional system. With the help of some fixed point theorems and the properties of the Green function, we establish several sets of sufficient conditions on the existence of positive solutions. The obtained results extend and include some existing ones and are illustrated with some examples for their feasibility.

  18. THE TRAVELLING SALESMAN PROBLEM IN THE ENGINEERING EDUCATION PROGRAMMING CURRICULUM

    Directory of Open Access Journals (Sweden)

    Yevgeny Gayev

    2017-11-01

    Full Text Available Objective: To make students familiar with the famous Traveling Salesman Problem (TSP and suggest the latter to become a common exercise in engineering programming curriculum provided the students master computer science in the easy programming environment MATLAB. Methods: easy programming in MATLAB makes true such modern educational approach as “discovery based” methodology. Results: a MATLAB TSP-program oriented to Ukrainian map is suggested that allows to pictorially demonstrate the process of optimal route search with an option to decelerate or accelerate the demonstration. The program is guessed to be useful both for learning the TSP as one of fundamental logistics problems and as an intriguing programming curriculum excersize. Several sub-programs according to key stone Computer Science Curriculum have also been suggested. This lies in line with recent “discovery based” learning methodology. Discussion: we explain how to create this program for visual discrete optimization, suggest required subprograms belonging to key stone programming algorithms including rather modern graphical user interface (GUI, how to use this MATLAB TSP-program for demonstration the drastical grows of solution time required. Conclusions: easy programming being realized in MATLAB makes dificult curriculum problems attractive to students; it focuses them to main problem’ features, laws and algorithms implementing the “discovery based” methodology in such a way.

  19. A "feasible direction" search for Lineal Programming problem solving

    Directory of Open Access Journals (Sweden)

    Jaime U Malpica Angarita

    2003-07-01

    Full Text Available The study presents an approach to solve linear programming problems with no artificial variables. A primal linear minimization problem is standard form and its associated dual linear maximization problem are used. Initially, the dual (or a partial dual program is solved by a "feasible direction" search, where the Karush-Kuhn-Tucker conditions help to verify its optimality and then its feasibility. The "feasible direction" search exploits the characteristics of the convex polyhedron (or prototype formed by the dual program constraints to find a starting point and then follows line segments, whose directions are found in afine subspaces defined by boundary hyperplanes of polyhedral faces, to find next points up to the (an optimal one. Them, the remaining dual constraints not satisfaced at that optimal dual point, if there are any, are handled as nonbasic variables of the primal program, which is to be solved by such "feasible direction" search.

  20. A New Nonlinear Unit Root Test with Fourier Function

    OpenAIRE

    Güriş, Burak

    2017-01-01

    Traditional unit root tests display a tendency to be nonstationary in the case of structural breaks and nonlinearity. To eliminate this problem this paper proposes a new flexible Fourier form nonlinear unit root test. This test eliminates this problem to add structural breaks and nonlinearity together to the test procedure. In this test procedure, structural breaks are modeled by means of a Fourier function and nonlinear adjustment is modeled by means of an Exponential Smooth Threshold Autore...

  1. An introduction to fuzzy linear programming problems theory, methods and applications

    CERN Document Server

    Kaur, Jagdeep

    2016-01-01

    The book presents a snapshot of the state of the art in the field of fully fuzzy linear programming. The main focus is on showing current methods for finding the fuzzy optimal solution of fully fuzzy linear programming problems in which all the parameters and decision variables are represented by non-negative fuzzy numbers. It presents new methods developed by the authors, as well as existing methods developed by others, and their application to real-world problems, including fuzzy transportation problems. Moreover, it compares the outcomes of the different methods and discusses their advantages/disadvantages. As the first work to collect at one place the most important methods for solving fuzzy linear programming problems, the book represents a useful reference guide for students and researchers, providing them with the necessary theoretical and practical knowledge to deal with linear programming problems under uncertainty.

  2. Computational Performance Analysis of Nonlinear Dynamic Systems using Semi-infinite Programming

    Directory of Open Access Journals (Sweden)

    Tor A. Johansen

    2001-01-01

    Full Text Available For nonlinear systems that satisfy certain regularity conditions it is shown that upper and lower bounds on the performance (cost function can be computed using linear or quadratic programming. The performance conditions derived from Hamilton-Jacobi inequalities are formulated as linear inequalities defined pointwise by discretizing the state-space when assuming a linearly parameterized class of functions representing the candidate performance bounds. Uncertainty with respect to some system parameters can be incorporated by also gridding the parameter set. In addition to performance analysis, the method can also be used to compute Lyapunov functions that guarantees uniform exponential stability.

  3. Optimal Decision-Making in Fuzzy Economic Order Quantity (EOQ Model under Restricted Space: A Non-Linear Programming Approach

    Directory of Open Access Journals (Sweden)

    M. Pattnaik

    2013-08-01

    Full Text Available In this paper the concept of fuzzy Non-Linear Programming Technique is applied to solve an economic order quantity (EOQ model under restricted space. Since various types of uncertainties and imprecision are inherent in real inventory problems they are classically modeled using the approaches from the probability theory. However, there are uncertainties that cannot be appropriately treated by usual probabilistic models. The questions how to define inventory optimization tasks in such environment how to interpret optimal solutions arise. This paper allows the modification of the Single item EOQ model in presence of fuzzy decision making process where demand is related to the unit price and the setup cost varies with the quantity produced/Purchased. This paper considers the modification of objective function and storage area in the presence of imprecisely estimated parameters. The model is developed for the problem by employing different modeling approaches over an infinite planning horizon. It incorporates all concepts of a fuzzy arithmetic approach, the quantity ordered and the demand per unit compares both fuzzy non linear and other models. Investigation of the properties of an optimal solution allows developing an algorithm whose validity is illustrated through an example problem and ugh MATLAB (R2009a version software, the two and three dimensional diagrams are represented to the application. Sensitivity analysis of the optimal solution is also studied with respect to changes in different parameter values and to draw managerial insights of the decision problem.

  4. Nonlinear surface Alfven waves

    International Nuclear Information System (INIS)

    Cramer, N.F.

    1991-01-01

    The problem of nonlinear surface Alfven waves propagating on an interface between a plasma and a vacuum is discussed, with dispersion provided by the finite-frequency effect, i.e. the finite ratio of the frequency to the ion-cyclotron frequency. A set of simplified nonlinear wave equations is derived using the method of stretched co-ordinates, and another approach uses the generation of a second-harmonic wave and its interaction with the first harmonic to obtain a nonlinear dispersion relation. A nonlinear Schroedinger equation is then derived, and soliton solutions found that propagate as solitary pulses in directions close to parallel and antiparallel to the background magnetic field. (author)

  5. Nonlinear Physics of Plasmas

    CERN Document Server

    Kono, Mitsuo

    2010-01-01

    A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.

  6. Automatic Design of Synthetic Gene Circuits through Mixed Integer Non-linear Programming

    Science.gov (United States)

    Huynh, Linh; Kececioglu, John; Köppe, Matthias; Tagkopoulos, Ilias

    2012-01-01

    Automatic design of synthetic gene circuits poses a significant challenge to synthetic biology, primarily due to the complexity of biological systems, and the lack of rigorous optimization methods that can cope with the combinatorial explosion as the number of biological parts increases. Current optimization methods for synthetic gene design rely on heuristic algorithms that are usually not deterministic, deliver sub-optimal solutions, and provide no guaranties on convergence or error bounds. Here, we introduce an optimization framework for the problem of part selection in synthetic gene circuits that is based on mixed integer non-linear programming (MINLP), which is a deterministic method that finds the globally optimal solution and guarantees convergence in finite time. Given a synthetic gene circuit, a library of characterized parts, and user-defined constraints, our method can find the optimal selection of parts that satisfy the constraints and best approximates the objective function given by the user. We evaluated the proposed method in the design of three synthetic circuits (a toggle switch, a transcriptional cascade, and a band detector), with both experimentally constructed and synthetic promoter libraries. Scalability and robustness analysis shows that the proposed framework scales well with the library size and the solution space. The work described here is a step towards a unifying, realistic framework for the automated design of biological circuits. PMID:22536398

  7. Recent topics in nonlinear PDE

    International Nuclear Information System (INIS)

    Mimura, Masayasu; Nishida, Takaaki

    1984-01-01

    The meeting on the subject of nonlinear partial differential equations was held at Hiroshima University in February, 1983. Leading and active mathematicians were invited to talk on their current research interests in nonlinear pdes occuring in the areas of fluid dynamics, free boundary problems, population dynamics and mathematical physics. This volume contains the theory of nonlinear pdes and the related topics which have been recently developed in Japan. (Auth.)

  8. Regularity of the solutions to a nonlinear boundary problem with indefinite weight

    Directory of Open Access Journals (Sweden)

    Aomar Anane

    2011-01-01

    Full Text Available In this paper we study the regularity of the solutions to the problemDelta_p u = |u|^{p−2}u in the bounded smooth domainOmega ⊂ R^N,with|∇u|^{p−2} partial_{nu} u = lambda V (x|u|^{p−2}u + h as a nonlinear boundary condition, where partial Omega is C^{2,beta}, with beta ∈]0, 1[, and V is a weight in L^s(partial Omega and h ∈ L^s(partial Omega for some s ≥ 1. We prove that all solutions are in L^{infty}(Omega cap L^{infty}(Omega, and using the D.Debenedetto’s theorem of regularity in [1] we conclude that those solutions are in C^{1,alpha} overline{Omega} for some alpha ∈ ]0, 1[.

  9. On the Uniqueness of Solutions of a Nonlinear Elliptic Problem Arising in the Confinement of a Plasma in a Stellarator Device

    International Nuclear Information System (INIS)

    Diaz, J. I.; Galiano, G.; Padial, J. F.

    1999-01-01

    We study the uniqueness of solutions of a semilinear elliptic problem obtained from an inverse formulation when the nonlinear terms of the equation are prescribed in a general class of real functions. The inverse problem arises in the modeling of the magnetic confinement of a plasma in a Stellarator device. The uniqueness proof relies on an L ∞ -estimate on the solution of an auxiliary nonlocal problem formulated in terms of the relative rearrangement of a datum with respect to the solution

  10. Time history nonlinear earthquake response analysis considering materials and geometrical nonlinearity

    International Nuclear Information System (INIS)

    Kobayashi, T.; Yoshikawa, K.; Takaoka, E.; Nakazawa, M.; Shikama, Y.

    2002-01-01

    A time history nonlinear earthquake response analysis method was proposed and applied to earthquake response prediction analysis for a Large Scale Seismic Test (LSST) Program in Hualien, Taiwan, in which a 1/4 scale model of a nuclear reactor containment structure was constructed on sandy gravel layer. In the analysis both of strain-dependent material nonlinearity, and geometrical nonlinearity by base mat uplift, were considered. The 'Lattice Model' for the soil-structure interaction model was employed. An earthquake record on soil surface at the site was used as control motion, and deconvoluted to the input motion of the analysis model at GL-52 m with 300 Gal of maximum acceleration. The following two analyses were considered: (A) time history nonlinear, (B) equivalent linear, and the advantage of time history nonlinear earthquake response analysis method is discussed

  11. Some current topics on nonlinear conservation laws lectures at the morningside center of mathematics, 1

    CERN Document Server

    Hsiao, Ling

    2000-01-01

    This volume resulted from a year-long program at the Morningside Center of Mathematics at the Academia Sinica in Beijing. It presents an overview of nonlinear conversation laws and introduces developments in this expanding field. Xin's introductory overview of the subject is followed by lecture notes of leading experts who have made fundamental contributions to this field of research. A. Bressan's theory of L^1-well-posedness for entropy weak solutions to systems of nonlinear hyperbolic conversation laws in the class of viscosity solutions is one of the most important results in the past two decades; G. Chen discusses weak convergence methods and various applications to many problems; P. Degond details mathematical modelling of semi-conductor devices; B. Perthame describes the theory of asymptotic equivalence between conservation laws and singular kinetic equations; Z. Xin outlines the recent development of the vanishing viscosity problem and nonlinear stability of elementary wave-a major focus of research in...

  12. Numerical simulation of a nonlinear coupled fluid-structure problem. Application to the design of naval nuclear propulsion structures; Modelisation et simulation numerique d'un probleme couple fluide/structure non lineaire: application au dimensionnement de structures nucleaires de propulsion navale

    Energy Technology Data Exchange (ETDEWEB)

    Sigrist, J.F

    2004-11-15

    The present work deals with the numerical simulation of a coupled fluid/structure problem with fluid free surface. A generic coupled fluid/structure system is defined, on which a linear problem (modal analysis) and a non-linear problem (temporal analysis) are stated. In the linear case, a strong coupled method is used. It is based on a finite element approach of the structure problem and a finite or a boundary element approach of the fluid problem. The coupled problem is formulated in terms of pressure and displacement, leading to a non-symmetric problem which is solved with an appropriate algorithm. In the non-linear case, the structure problem is described with non-linear equations of motion, whereas the fluid problem is modeled with the Stokes equations. The numerical resolution of the coupled problem is based on a weak coupling procedure. The fluid problem is solved with a finite volume technique, using a moving mesh technique to adjust the structure motion, a VOF method for the description of the free surface and the PISO algorithm for the time integration. The structure problem is solved with a finite element technique, using an explicit/implicit time integration algorithm. A procedure is developed in order to handle the coupling in space (fluid forces and structure displacement exchanges between fluid and structure mesh, fluid re-meshing) and in time (staggered explicit algorithm, dynamic filtering of numerical oscillations). The non linear coupled problem is solved using a CFD code, whose use for FSI problem is validated with a benchmark presented in this work. A comparison is proposed between numerical results and analytical solution for two elementary fluid problems. The validation process can be applied for any CFD numerical code. A numerical study is then proposed on the generic coupled case in order to describe the fluid/structure interaction phenomenon (added mass, displaced mass, mode coupling, influence of structural non-linearity). An industrial

  13. Linear Programming and Its Application to Pattern Recognition Problems

    Science.gov (United States)

    Omalley, M. J.

    1973-01-01

    Linear programming and linear programming like techniques as applied to pattern recognition problems are discussed. Three relatively recent research articles on such applications are summarized. The main results of each paper are described, indicating the theoretical tools needed to obtain them. A synopsis of the author's comments is presented with regard to the applicability or non-applicability of his methods to particular problems, including computational results wherever given.

  14. Emotion Oriented Programming: Computational Abstractions for AI Problem Solving

    OpenAIRE

    Darty , Kevin; Sabouret , Nicolas

    2012-01-01

    International audience; In this paper, we present a programming paradigm for AI problem solving based on computational concepts drawn from Affective Computing. It is believed that emotions participate in human adaptability and reactivity, in behaviour selection and in complex and dynamic environments. We propose to define a mechanism inspired from this observation for general AI problem solving. To this purpose, we synthesize emotions as programming abstractions that represent the perception ...

  15. SPARSE ELECTROMAGNETIC IMAGING USING NONLINEAR LANDWEBER ITERATIONS

    KAUST Repository

    Desmal, Abdulla

    2015-07-29

    A scheme for efficiently solving the nonlinear electromagnetic inverse scattering problem on sparse investigation domains is described. The proposed scheme reconstructs the (complex) dielectric permittivity of an investigation domain from fields measured away from the domain itself. Least-squares data misfit between the computed scattered fields, which are expressed as a nonlinear function of the permittivity, and the measured fields is constrained by the L0/L1-norm of the solution. The resulting minimization problem is solved using nonlinear Landweber iterations, where at each iteration a thresholding function is applied to enforce the sparseness-promoting L0/L1-norm constraint. The thresholded nonlinear Landweber iterations are applied to several two-dimensional problems, where the ``measured\\'\\' fields are synthetically generated or obtained from actual experiments. These numerical experiments demonstrate the accuracy, efficiency, and applicability of the proposed scheme in reconstructing sparse profiles with high permittivity values.

  16. A cutting- plane approach for semi- infinite mathematical programming

    African Journals Online (AJOL)

    Many situations ranging from industrial to social via economic and environmental problems may be cast into a Semi-infinite mathematical program. In this paper, the cutting-plane approach which lends itself better for standard non-linear programs is exploited with good reasons for grappling with linear, convex and ...

  17. Cascaded nonlinearities for ultrafast nonlinear optical science and applications

    DEFF Research Database (Denmark)

    Bache, Morten

    the cascading nonlinearity is investigated in detail, especially with focus on femtosecond energetic laser pulses being subjected to this nonlinear response. Analytical, numerical and experimental results are used to understand the cascading interaction and applications are demonstrated. The defocusing soliton...... observations with analogies in fiber optics are observed numerically and experimentally, including soliton self-compression, soliton-induced resonant radiation, supercontinuum generation, optical wavebreaking and shock-front formation. All this happens despite no waveguide being present, thanks...... is of particular interest here, since it is quite unique and provides the solution to a number of standing challenges in the ultrafast nonlinear optics community. It solves the problem of catastrophic focusing and formation of a filaments in bulk glasses, which even under controlled circumstances is limited...

  18. AD Model Builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear models

    DEFF Research Database (Denmark)

    Fournier, David A.; Skaug, Hans J.; Ancheta, Johnoel

    2011-01-01

    Many criteria for statistical parameter estimation, such as maximum likelihood, are formulated as a nonlinear optimization problem.Automatic Differentiation Model Builder (ADMB) is a programming framework based on automatic differentiation, aimed at highly nonlinear models with a large number...... of such a feature is the generic implementation of Laplace approximation of high-dimensional integrals for use in latent variable models. We also review the literature in which ADMB has been used, and discuss future development of ADMB as an open source project. Overall, the main advantages ofADMB are flexibility...

  19. Non-linear finite element analysis in structural mechanics

    CERN Document Server

    Rust, Wilhelm

    2015-01-01

    This monograph describes the numerical analysis of non-linearities in structural mechanics, i.e. large rotations, large strain (geometric non-linearities), non-linear material behaviour, in particular elasto-plasticity as well as time-dependent behaviour, and contact. Based on that, the book treats stability problems and limit-load analyses, as well as non-linear equations of a large number of variables. Moreover, the author presents a wide range of problem sets and their solutions. The target audience primarily comprises advanced undergraduate and graduate students of mechanical and civil engineering, but the book may also be beneficial for practising engineers in industry.

  20. General purpose nonlinear analysis program FINAS for elevated temperature design of FBR components

    International Nuclear Information System (INIS)

    Iwata, K.; Atsumo, H.; Kano, T.; Takeda, H.

    1982-01-01

    This paper presents currently available capabilities of a general purpose finite element nonlinear analysis program FINAS (FBR Inelastic Structural Analysis System) which has been developed at Power Reactor and Nuclear Fuel Development Corporation (PNC) since 1976 to support structural design of fast breeder reactor (FBR) components in Japan. This program is capable of treating inelastic responses of arbitrary complex structures subjected to static and dynamic load histories. Various types of finite element covering rods, beams, pipes, axisymmetric, two and three dimensional solids, plates and shells, are implemented in the program. The thermal elastic-plastic creep analysis is possible for each element type, with primary emphasis on the application to FBR components subjected to sustained or cyclic loads at elevated temperature. The program permits large deformation, buckling, fracture mechanics, and dynamic analyses for some of the element types and provides a number of options for automatic mesh generation and computer graphics. Some examples including elevated temperature effects are shown to demonstrate the accuracy and the efficiency of the program

  1. Programming languages for business problem solving

    CERN Document Server

    Wang, Shouhong

    2007-01-01

    It has become crucial for managers to be computer literate in today's business environment. It is also important that those entering the field acquire the fundamental theories of information systems, the essential practical skills in computer applications, and the desire for life-long learning in information technology. Programming Languages for Business Problem Solving presents a working knowledge of the major programming languages, including COBOL, C++, Java, HTML, JavaScript, VB.NET, VBA, ASP.NET, Perl, PHP, XML, and SQL, used in the current business computing environment. The book examin

  2. Nonlinear filtering for LIDAR signal processing

    Directory of Open Access Journals (Sweden)

    D. G. Lainiotis

    1996-01-01

    Full Text Available LIDAR (Laser Integrated Radar is an engineering problem of great practical importance in environmental monitoring sciences. Signal processing for LIDAR applications involves highly nonlinear models and consequently nonlinear filtering. Optimal nonlinear filters, however, are practically unrealizable. In this paper, the Lainiotis's multi-model partitioning methodology and the related approximate but effective nonlinear filtering algorithms are reviewed and applied to LIDAR signal processing. Extensive simulation and performance evaluation of the multi-model partitioning approach and its application to LIDAR signal processing shows that the nonlinear partitioning methods are very effective and significantly superior to the nonlinear extended Kalman filter (EKF, which has been the standard nonlinear filter in past engineering applications.

  3. Approximate Solution of Nonlinear Klein-Gordon Equation Using Sobolev Gradients

    Directory of Open Access Journals (Sweden)

    Nauman Raza

    2016-01-01

    Full Text Available The nonlinear Klein-Gordon equation (KGE models many nonlinear phenomena. In this paper, we propose a scheme for numerical approximation of solutions of the one-dimensional nonlinear KGE. A common approach to find a solution of a nonlinear system is to first linearize the equations by successive substitution or the Newton iteration method and then solve a linear least squares problem. Here, we show that it can be advantageous to form a sum of squared residuals of the nonlinear problem and then find a zero of the gradient. Our scheme is based on the Sobolev gradient method for solving a nonlinear least square problem directly. The numerical results are compared with Lattice Boltzmann Method (LBM. The L2, L∞, and Root-Mean-Square (RMS values indicate better accuracy of the proposed method with less computational effort.

  4. Problem solving and Program design using the TI-92

    NARCIS (Netherlands)

    Ir.ing. Ton Marée; ir Martijn van Dongen

    2000-01-01

    This textbook is intended for a basic course in problem solving and program design needed by scientists and engineers using the TI-92. The TI-92 is an extremely powerful problem solving tool that can help you manage complicated problems quickly. We assume no prior knowledge of computers or

  5. Developing Student Programming and Problem-Solving Skills with Visual Basic

    Science.gov (United States)

    Siegle, Del

    2009-01-01

    Although most computer users will never need to write a computer program, many students enjoy the challenge of creating one. Computer programming enhances students' problem solving by forcing students to break a problem into its component pieces and reassemble it in a generic format that can be understood by a nonsentient entity. It promotes…

  6. Using Problem Solving to Teach a Programming Language.

    Science.gov (United States)

    Milbrandt, George

    1995-01-01

    Computer studies courses should incorporate as many computer concepts and programming language experiences as possible. A gradual increase in problem difficulty will help the student to understand various computer concepts, and the programming language's syntax and structure. A sidebar provides two examples of how to establish a learning…

  7. Convex models and probabilistic approach of nonlinear fatigue failure

    International Nuclear Information System (INIS)

    Qiu Zhiping; Lin Qiang; Wang Xiaojun

    2008-01-01

    This paper is concerned with the nonlinear fatigue failure problem with uncertainties in the structural systems. In the present study, in order to solve the nonlinear problem by convex models, the theory of ellipsoidal algebra with the help of the thought of interval analysis is applied. In terms of the inclusion monotonic property of ellipsoidal functions, the nonlinear fatigue failure problem with uncertainties can be solved. A numerical example of 25-bar truss structures is given to illustrate the efficiency of the presented method in comparison with the probabilistic approach

  8. Point source identification in nonlinear advection–diffusion–reaction systems

    International Nuclear Information System (INIS)

    Mamonov, A V; Tsai, Y-H R

    2013-01-01

    We consider a problem of identification of point sources in time-dependent advection–diffusion systems with a nonlinear reaction term. The linear counterpart of the problem in question can be reduced to solving a system of nonlinear algebraic equations via the use of adjoint equations. We extend this approach by constructing an algorithm that solves the problem iteratively to account for the nonlinearity of the reaction term. We study the question of improving the quality of source identification by adding more measurements adaptively using the solution obtained previously with a smaller number of measurements. (paper)

  9. An approach for solving linear fractional programming problems ...

    African Journals Online (AJOL)

    The paper presents a new approach for solving a fractional linear programming problem in which the objective function is a linear fractional function, while the constraint functions are in the form of linear inequalities. The approach adopted is based mainly upon solving the problem algebraically using the concept of duality ...

  10. Solving a class of generalized fractional programming problems using the feasibility of linear programs.

    Science.gov (United States)

    Shen, Peiping; Zhang, Tongli; Wang, Chunfeng

    2017-01-01

    This article presents a new approximation algorithm for globally solving a class of generalized fractional programming problems (P) whose objective functions are defined as an appropriate composition of ratios of affine functions. To solve this problem, the algorithm solves an equivalent optimization problem (Q) via an exploration of a suitably defined nonuniform grid. The main work of the algorithm involves checking the feasibility of linear programs associated with the interesting grid points. It is proved that the proposed algorithm is a fully polynomial time approximation scheme as the ratio terms are fixed in the objective function to problem (P), based on the computational complexity result. In contrast to existing results in literature, the algorithm does not require the assumptions on quasi-concavity or low-rank of the objective function to problem (P). Numerical results are given to illustrate the feasibility and effectiveness of the proposed algorithm.

  11. Nonlinear diffusion problem arising in plasma physics

    International Nuclear Information System (INIS)

    Berryman, J.G.; Holland, C.J.

    1978-01-01

    In earlier studies of plasma diffusion with Okuda-Dawson scaling (D approx. n/sup -1/2/), perturbation theory indicated that arbitrary initial data should evolve rapidly toward the separation solution of the relevant nonlinear diffusion equation. Now a Lyapunov functional has been found which is strictly decreasing in time and bounded below. The rigorous proof that arbitrary initial data evolve toeard the separable solution is summarized. Rigorous bounds on the decay time are also presented

  12. ABAQUS/EPGEN - a general purpose finite element code with emphasis on nonlinear applications

    International Nuclear Information System (INIS)

    Hibbitt, H.D.

    1984-01-01

    The article contains a summary description of ABAQUS, a finite element program designed for general use in nonlinear as well as linear structural problems, in the context of its application to nuclear structural integrity analysis. The article begins with a discussion of the design criteria and methods upon which the code development has been based. The engineering modelling capabilities, currently implemented in the program - elements, constitutive models and analysis procedures - are then described. Finally, a few demonstration examples are presented, to illustrate some of the program's features that are of interest in structural integrity analysis associated with nuclear power plants. (orig.)

  13. Theoretical and algorithmic advances in multi-parametric programming and control

    KAUST Repository

    Pistikopoulos, Efstratios N.; Dominguez, Luis; Panos, Christos; Kouramas, Konstantinos; Chinchuluun, Altannar

    2012-01-01

    This paper presents an overview of recent theoretical and algorithmic advances, and applications in the areas of multi-parametric programming and explicit/multi-parametric model predictive control (mp-MPC). In multi-parametric programming, advances include areas such as nonlinear multi-parametric programming (mp-NLP), bi-level programming, dynamic programming and global optimization for multi-parametric mixed-integer linear programming problems (mp-MILPs). In multi-parametric/explicit MPC (mp-MPC), advances include areas such as robust multi-parametric control, multi-parametric nonlinear MPC (mp-NMPC) and model reduction in mp-MPC. A comprehensive framework for multi-parametric programming and control is also presented. Recent applications include a hydrogen storage device, a fuel cell power generation system, an unmanned autonomous vehicle (UAV) and a hybrid pressure swing adsorption (PSA) system. © 2012 Springer-Verlag.

  14. Theoretical and algorithmic advances in multi-parametric programming and control

    KAUST Repository

    Pistikopoulos, Efstratios N.

    2012-04-21

    This paper presents an overview of recent theoretical and algorithmic advances, and applications in the areas of multi-parametric programming and explicit/multi-parametric model predictive control (mp-MPC). In multi-parametric programming, advances include areas such as nonlinear multi-parametric programming (mp-NLP), bi-level programming, dynamic programming and global optimization for multi-parametric mixed-integer linear programming problems (mp-MILPs). In multi-parametric/explicit MPC (mp-MPC), advances include areas such as robust multi-parametric control, multi-parametric nonlinear MPC (mp-NMPC) and model reduction in mp-MPC. A comprehensive framework for multi-parametric programming and control is also presented. Recent applications include a hydrogen storage device, a fuel cell power generation system, an unmanned autonomous vehicle (UAV) and a hybrid pressure swing adsorption (PSA) system. © 2012 Springer-Verlag.

  15. Multiple Positive Solutions of a Nonlinear Four-Point Singular Boundary Value Problem with a p-Laplacian Operator on Time Scales

    Directory of Open Access Journals (Sweden)

    Shihuang Hong

    2009-01-01

    Full Text Available We present sufficient conditions for the existence of at least twin or triple positive solutions of a nonlinear four-point singular boundary value problem with a p-Laplacian dynamic equation on a time scale. Our results are obtained via some new multiple fixed point theorems.

  16. Exact multiplicity results for quasilinear boundary-value problems with cubic-like nonlinearities

    Directory of Open Access Journals (Sweden)

    Idris Addou

    2000-01-01

    Full Text Available We consider the boundary-value problem $$displaylines{ -(varphi_p (u'' =lambda f(u mbox{ in }(0,1 cr u(0 = u(1 =0,, }$$ where $p>1$, $lambda >0$ and $varphi_p (x =| x|^{p-2}x$. The nonlinearity $f$ is cubic-like with three distinct roots 0=a less than b less than c. By means of a quadrature method, we provide the exact number of solutions for all $lambda >0$. This way we extend a recent result, for $p=2$, by Korman et al. cite{KormanLiOuyang} to the general case $p>1$. We shall prove that when 1less than $pleq 2$ the structure of the solution set is exactly the same as that studied in the case $p=2$ by Korman et al. cite{KormanLiOuyang}, and strictly different in the case $p>2$.

  17. A nonlinear boundary integral equations method for the solving of quasistatic elastic contact problem with Coulomb friction

    Directory of Open Access Journals (Sweden)

    Yurii M. Streliaiev

    2016-06-01

    Full Text Available Three-dimensional quasistatic contact problem of two linearly elastic bodies' interaction with Coulomb friction taken into account is considered. The boundary conditions of the problem have been simplified by the modification of the Coulomb's law of friction. This modification is based on the introducing of a delay in normal contact tractions that bound tangent contact tractions in the Coulomb's law of friction expressions. At this statement the problem is reduced to a sequence of similar systems of nonlinear integral equations describing bodies' interaction at each step of loading. A method for an approximate solution of the integral equations system corresponded to each step of loading is applied. This method consists of system regularization, discretization of regularized system and iterative process application for solving the discretized system. A numerical solution of a contact problem of an elastic sphere with an elastic half-space interaction under increasing and subsequently decreasing normal compressive force has been obtained.

  18. Nonlinear optics principles and applications

    CERN Document Server

    Rottwitt, Karsten

    2014-01-01

    IntroductionReview of linear opticsInduced polarizationHarmonic oscillator modelLocal field correctionsEstimated nonlinear responseSummaryTime-domain material responseThe polarization time-response functionThe Born-Oppenheimer approximationRaman scattering response function of silicaSummaryMaterial response in the frequency domain, susceptibility tensorsThe susceptibility tensorThe induced polarization in the frequency domainSum of monochromatic fieldsThe prefactor to the induced polarizationThird-order polarization in the Born-Oppenheimer approximation in the frequency domainKramers-Kronig relationsSummarySymmetries in nonlinear opticsSpatial symmetriesSecond-order materialsThird-order nonlinear materialsCyclic coordinate-systemContracted notation for second-order susceptibility tensorsSummaryThe nonlinear wave equationMono and quasi-monochromatic beamsPlane waves - the transverse problemWaveguidesVectorial approachNonlinear birefringenceSummarySecond-order nonlinear effectsGeneral theoryCoupled wave theoryP...

  19. Nonlinear differential equations

    CERN Document Server

    Struble, Raimond A

    2017-01-01

    Detailed treatment covers existence and uniqueness of a solution of the initial value problem, properties of solutions, properties of linear systems, stability of nonlinear systems, and two-dimensional systems. 1962 edition.

  20. Network science, nonlinear science and infrastructure systems

    CERN Document Server

    2007-01-01

    Network Science, Nonlinear Science and Infrastructure Systems has been written by leading scholars in these areas. Its express purpose is to develop common theoretical underpinnings to better solve modern infrastructural problems. It is felt by many who work in these fields that many modern communication problems, ranging from transportation networks to telecommunications, Internet, supply chains, etc., are fundamentally infrastructure problems. Moreover, these infrastructure problems would benefit greatly from a confluence of theoretical and methodological work done with the areas of Network Science, Dynamical Systems and Nonlinear Science. This book is dedicated to the formulation of infrastructural tools that will better solve these types of infrastructural problems. .

  1. Finite elements of nonlinear continua

    CERN Document Server

    Oden, John Tinsley

    1972-01-01

    Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s

  2. A Comparative Study of Three Different Mathematical Methods for Solving the Unit Commitment Problem

    Directory of Open Access Journals (Sweden)

    Mehmet Kurban

    2009-01-01

    Full Text Available The unit commitment (UC problem which is an important subject in power system engineering is solved by using Lagragian relaxation (LR, penalty function (PF, and augmented Lagrangian penalty function (ALPF methods due to their higher solution quality and faster computational time than metaheuristic approaches. This problem is considered to be a nonlinear programming-(NP- hard problem because it is nonlinear, mixed-integer, and nonconvex. These three methods used for solving the problem are based on dual optimization techniques. ALPF method which combines the algorithmic aspects of both LR and PF methods is firstly used for solving the UC problem. These methods are compared to each other based on feasible schedule for each stage, feasible cost, dual cost, duality gap, duration time, and number of iterations. The numerical results show that the ALPF method gives the best duality gap, feasible and dual cost instead of worse duration time and the number of iterations. The four-unit Tuncbilek thermal plant which is located in Kutahya region in Turkey is chosen as a test system in this study. The programs used for all the analyses are coded and implemented using general algebraic modeling system (GAMS.

  3. Bricolage Programming and Problem Solving Ability in Young Children : an Exploratory Study

    OpenAIRE

    Rose, Simon

    2016-01-01

    Visual programming environments, such as Scratch, are increasingly being used by schools to teach problem solving and computational thinking skills. However, academic research is divided on the effect that visual programming has on problem solving in a computational context. This paper focuses on the role of bricolage programming in this debate; a bottom-up programming approach that arises when using block-style programming interfaces. Bricolage programming was a term originally used to descr...

  4. Advances in iterative methods for nonlinear equations

    CERN Document Server

    Busquier, Sonia

    2016-01-01

    This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations...

  5. Applications of Automation Methods for Nonlinear Fracture Test Analysis

    Science.gov (United States)

    Allen, Phillip A.; Wells, Douglas N.

    2013-01-01

    Using automated and standardized computer tools to calculate the pertinent test result values has several advantages such as: 1. allowing high-fidelity solutions to complex nonlinear phenomena that would be impractical to express in written equation form, 2. eliminating errors associated with the interpretation and programing of analysis procedures from the text of test standards, 3. lessening the need for expertise in the areas of solid mechanics, fracture mechanics, numerical methods, and/or finite element modeling, to achieve sound results, 4. and providing one computer tool and/or one set of solutions for all users for a more "standardized" answer. In summary, this approach allows a non-expert with rudimentary training to get the best practical solution based on the latest understanding with minimum difficulty.Other existing ASTM standards that cover complicated phenomena use standard computer programs: 1. ASTM C1340/C1340M-10- Standard Practice for Estimation of Heat Gain or Loss Through Ceilings Under Attics Containing Radiant Barriers by Use of a Computer Program 2. ASTM F 2815 - Standard Practice for Chemical Permeation through Protective Clothing Materials: Testing Data Analysis by Use of a Computer Program 3. ASTM E2807 - Standard Specification for 3D Imaging Data Exchange, Version 1.0 The verification, validation, and round-robin processes required of a computer tool closely parallel the methods that are used to ensure the solution validity for equations included in test standard. The use of automated analysis tools allows the creation and practical implementation of advanced fracture mechanics test standards that capture the physics of a nonlinear fracture mechanics problem without adding undue burden or expense to the user. The presented approach forms a bridge between the equation-based fracture testing standards of today and the next generation of standards solving complex problems through analysis automation.

  6. Optimization of constrained multiple-objective reliability problems using evolutionary algorithms

    International Nuclear Information System (INIS)

    Salazar, Daniel; Rocco, Claudio M.; Galvan, Blas J.

    2006-01-01

    This paper illustrates the use of multi-objective optimization to solve three types of reliability optimization problems: to find the optimal number of redundant components, find the reliability of components, and determine both their redundancy and reliability. In general, these problems have been formulated as single objective mixed-integer non-linear programming problems with one or several constraints and solved by using mathematical programming techniques or special heuristics. In this work, these problems are reformulated as multiple-objective problems (MOP) and then solved by using a second-generation Multiple-Objective Evolutionary Algorithm (MOEA) that allows handling constraints. The MOEA used in this paper (NSGA-II) demonstrates the ability to identify a set of optimal solutions (Pareto front), which provides the Decision Maker with a complete picture of the optimal solution space. Finally, the advantages of both MOP and MOEA approaches are illustrated by solving four redundancy problems taken from the literature

  7. Optimization of constrained multiple-objective reliability problems using evolutionary algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Salazar, Daniel [Instituto de Sistemas Inteligentes y Aplicaciones Numericas en Ingenieria (IUSIANI), Division de Computacion Evolutiva y Aplicaciones (CEANI), Universidad de Las Palmas de Gran Canaria, Islas Canarias (Spain) and Facultad de Ingenieria, Universidad Central Venezuela, Caracas (Venezuela)]. E-mail: danielsalazaraponte@gmail.com; Rocco, Claudio M. [Facultad de Ingenieria, Universidad Central Venezuela, Caracas (Venezuela)]. E-mail: crocco@reacciun.ve; Galvan, Blas J. [Instituto de Sistemas Inteligentes y Aplicaciones Numericas en Ingenieria (IUSIANI), Division de Computacion Evolutiva y Aplicaciones (CEANI), Universidad de Las Palmas de Gran Canaria, Islas Canarias (Spain)]. E-mail: bgalvan@step.es

    2006-09-15

    This paper illustrates the use of multi-objective optimization to solve three types of reliability optimization problems: to find the optimal number of redundant components, find the reliability of components, and determine both their redundancy and reliability. In general, these problems have been formulated as single objective mixed-integer non-linear programming problems with one or several constraints and solved by using mathematical programming techniques or special heuristics. In this work, these problems are reformulated as multiple-objective problems (MOP) and then solved by using a second-generation Multiple-Objective Evolutionary Algorithm (MOEA) that allows handling constraints. The MOEA used in this paper (NSGA-II) demonstrates the ability to identify a set of optimal solutions (Pareto front), which provides the Decision Maker with a complete picture of the optimal solution space. Finally, the advantages of both MOP and MOEA approaches are illustrated by solving four redundancy problems taken from the literature.

  8. A non-linear branch and cut method for solving discrete minimum compliance problems to global optimality

    DEFF Research Database (Denmark)

    Stolpe, Mathias; Bendsøe, Martin P.

    2007-01-01

    This paper present some initial results pertaining to a search for globally optimal solutions to a challenging benchmark example proposed by Zhou and Rozvany. This means that we are dealing with global optimization of the classical single load minimum compliance topology design problem with a fixed...... finite element discretization and with discrete design variables. Global optimality is achieved by the implementation of some specially constructed convergent nonlinear branch and cut methods, based on the use of natural relaxations and by applying strengthening constraints (linear valid inequalities...

  9. NONLINEAR DYNAMICS OF ORGANIZATION DEVELOPMENT

    Directory of Open Access Journals (Sweden)

    Денис Антонович БУШУЕВ

    2016-02-01

    Full Text Available The nonlinear behavior of organizations in development projects is considered. The nonlinear behavior is initiated in the growth of organizations and requires a restructuring of governance in identifying dysfunctions. Such a restructuring is needed in the area of soft components, determining the organizational levels of competence in the management of projects, programs, portfolios and heads of the Project Management Office. An important component of the strategic development of the organization is the proposed concept for formation and management of development programs in the context according to their life cycle. It should take into account the non-linear behavior of the soft components of the system and violation of functional processes of the organization. The specific management syndromes of projects and programs are considered. Such as syndromes time management project linked to the singular points of the project. These syndromes are "shift to the right", "point of no return", "braking at the end of the project" and others.

  10. MULTI-CRITERIA PROGRAMMING METHODS AND PRODUCTION PLAN OPTIMIZATION PROBLEM SOLVING IN METAL INDUSTRY

    Directory of Open Access Journals (Sweden)

    Tunjo Perić

    2017-09-01

    Full Text Available This paper presents the production plan optimization in the metal industry considered as a multi-criteria programming problem. We first provided the definition of the multi-criteria programming problem and classification of the multicriteria programming methods. Then we applied two multi-criteria programming methods (the STEM method and the PROMETHEE method in solving a problem of multi-criteria optimization production plan in a company from the metal industry. The obtained results indicate a high efficiency of the applied methods in solving the problem.

  11. Controllability of nonlinear delay oscillating systems

    Directory of Open Access Journals (Sweden)

    Chengbin Liang

    2017-05-01

    Full Text Available In this paper, we study the controllability of a system governed by second order delay differential equations. We introduce a delay Gramian matrix involving the delayed matrix sine, which is used to establish sufficient and necessary conditions of controllability for the linear problem. In addition, we also construct a specific control function for controllability. For the nonlinear problem, we construct a control function and transfer the controllability problem to a fixed point problem for a suitable operator. We give a sufficient condition to guarantee the nonlinear delay system is controllable. Two examples are given to illustrate our theoretical results by calculating a specific control function and inverse of a delay Gramian matrix.

  12. DESIGN OF EDUCATIONAL PROBLEMS ON LINEAR PROGRAMMING USING SYSTEMS OF COMPUTER MATHEMATICS

    Directory of Open Access Journals (Sweden)

    Volodymyr M. Mykhalevych

    2013-11-01

    Full Text Available From a perspective of the theory of educational problems a problem of substitution in the conditions of ICT use of one discipline by an educational problem of another discipline is represented. Through the example of mathematical problems of linear programming it is showed that a student’s method of operation in the course of an educational problem solving is determinant in the identification of an educational problem in relation to a specific discipline: linear programming, informatics, mathematical modeling, methods of optimization, automatic control theory, calculus etc. It is substantiated the necessity of linear programming educational problems renovation with the purpose of making students free of bulky similar arithmetic calculations and notes which often becomes a barrier to a deeper understanding of key ideas taken as a basis of algorithms used by them.

  13. Methodology for global nonlinear analysis of nuclear systems

    International Nuclear Information System (INIS)

    Cacuci, D.G.; Cacuci, G.L.

    1987-01-01

    This paper outlines a general method for globally computing the crucial features of nonlinear problems: bifurcations, limit points, saddle points, extrema (maxima and minima); our method also yields the local sensitivities (i.e., first order derivatives) of the system's state variables (e.g., fluxes, power, temperatures, flows) at any point in the system's phase space. We also present an application of this method to the nonlinear BWR model discussed in Refs. 8 and 11. The most significant novel feature of our method is the recasting of a general mathematical problem comprising three aspects: (1) nonlinear constrained optimization, (2) sensitivity analysis, into a fixed point problem of the form F[u(s), λ(s)] = 0 whose global zeros and singular points are related to the special features (i.e., extrema, bifurcations, etc.) of the original problem

  14. Micosoft Excel Sensitivity Analysis for Linear and Stochastic Program Feed Formulation

    Science.gov (United States)

    Sensitivity analysis is a part of mathematical programming solutions and is used in making nutritional and economic decisions for a given feed formulation problem. The terms, shadow price and reduced cost, are familiar linear program (LP) terms to feed formulators. Because of the nonlinear nature of...

  15. Multidimensional nonlinear descriptive analysis

    CERN Document Server

    Nishisato, Shizuhiko

    2006-01-01

    Quantification of categorical, or non-numerical, data is a problem that scientists face across a wide range of disciplines. Exploring data analysis in various areas of research, such as the social sciences and biology, Multidimensional Nonlinear Descriptive Analysis presents methods for analyzing categorical data that are not necessarily sampled randomly from a normal population and often involve nonlinear relations. This reference not only provides an overview of multidimensional nonlinear descriptive analysis (MUNDA) of discrete data, it also offers new results in a variety of fields. The first part of the book covers conceptual and technical preliminaries needed to understand the data analysis in subsequent chapters. The next two parts contain applications of MUNDA to diverse data types, with each chapter devoted to one type of categorical data, a brief historical comment, and basic skills peculiar to the data types. The final part examines several problems and then concludes with suggestions for futu...

  16. Sparse Reconstruction Schemes for Nonlinear Electromagnetic Imaging

    KAUST Repository

    Desmal, Abdulla

    2016-03-01

    Electromagnetic imaging is the problem of determining material properties from scattered fields measured away from the domain under investigation. Solving this inverse problem is a challenging task because (i) it is ill-posed due to the presence of (smoothing) integral operators used in the representation of scattered fields in terms of material properties, and scattered fields are obtained at a finite set of points through noisy measurements; and (ii) it is nonlinear simply due the fact that scattered fields are nonlinear functions of the material properties. The work described in this thesis tackles the ill-posedness of the electromagnetic imaging problem using sparsity-based regularization techniques, which assume that the scatterer(s) occupy only a small fraction of the investigation domain. More specifically, four novel imaging methods are formulated and implemented. (i) Sparsity-regularized Born iterative method iteratively linearizes the nonlinear inverse scattering problem and each linear problem is regularized using an improved iterative shrinkage algorithm enforcing the sparsity constraint. (ii) Sparsity-regularized nonlinear inexact Newton method calls for the solution of a linear system involving the Frechet derivative matrix of the forward scattering operator at every iteration step. For faster convergence, the solution of this matrix system is regularized under the sparsity constraint and preconditioned by leveling the matrix singular values. (iii) Sparsity-regularized nonlinear Tikhonov method directly solves the nonlinear minimization problem using Landweber iterations, where a thresholding function is applied at every iteration step to enforce the sparsity constraint. (iv) This last scheme is accelerated using a projected steepest descent method when it is applied to three-dimensional investigation domains. Projection replaces the thresholding operation and enforces the sparsity constraint. Numerical experiments, which are carried out using

  17. Applications of nonlinear fiber optics

    CERN Document Server

    Agrawal, Govind

    2008-01-01

    * The only book describing applications of nonlinear fiber optics * Two new chapters on the latest developments: highly nonlinear fibers and quantum applications* Coverage of biomedical applications* Problems provided at the end of each chapterThe development of new highly nonlinear fibers - referred to as microstructured fibers, holey fibers and photonic crystal fibers - is the next generation technology for all-optical signal processing and biomedical applications. This new edition has been thoroughly updated to incorporate these key technology developments.The bo

  18. Nonlinear optimization

    CERN Document Server

    Ruszczynski, Andrzej

    2011-01-01

    Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...

  19. Logo Programming, Problem Solving, and Knowledge-Based Instruction.

    Science.gov (United States)

    Swan, Karen; Black, John B.

    The research reported in this paper was designed to investigate the hypothesis that computer programming may support the teaching and learning of problem solving, but that to do so, problem solving must be explicitly taught. Three studies involved students in several grades: 4th, 6th, 8th, 11th, and 12th. Findings collectively show that five…

  20. Advances in dynamic relaxation techniques for nonlinear finite element analysis

    International Nuclear Information System (INIS)

    Sauve, R.G.; Metzger, D.R.

    1995-01-01

    Traditionally, the finite element technique has been applied to static and steady-state problems using implicit methods. When nonlinearities exist, equilibrium iterations must be performed using Newton-Raphson or quasi-Newton techniques at each load level. In the presence of complex geometry, nonlinear material behavior, and large relative sliding of material interfaces, solutions using implicit methods often become intractable. A dynamic relaxation algorithm is developed for inclusion in finite element codes. The explicit nature of the method avoids large computer memory requirements and makes possible the solution of large-scale problems. The method described approaches the steady-state solution with no overshoot, a problem which has plagued researchers in the past. The method is included in a general nonlinear finite element code. A description of the method along with a number of new applications involving geometric and material nonlinearities are presented. They include: (1) nonlinear geometric cantilever plate; (2) moment-loaded nonlinear beam; and (3) creep of nuclear fuel channel assemblies

  1. MULTI-CRITERIA PROGRAMMING METHODS AND PRODUCTION PLAN OPTIMIZATION PROBLEM SOLVING IN METAL INDUSTRY

    OpenAIRE

    Tunjo Perić; Željko Mandić

    2017-01-01

    This paper presents the production plan optimization in the metal industry considered as a multi-criteria programming problem. We first provided the definition of the multi-criteria programming problem and classification of the multicriteria programming methods. Then we applied two multi-criteria programming methods (the STEM method and the PROMETHEE method) in solving a problem of multi-criteria optimization production plan in a company from the metal industry. The obtained resul...

  2. Spurious Solutions Of Nonlinear Differential Equations

    Science.gov (United States)

    Yee, H. C.; Sweby, P. K.; Griffiths, D. F.

    1992-01-01

    Report utilizes nonlinear-dynamics approach to investigate possible sources of errors and slow convergence and non-convergence of steady-state numerical solutions when using time-dependent approach for problems containing nonlinear source terms. Emphasizes implications for development of algorithms in CFD and computational sciences in general. Main fundamental conclusion of study is that qualitative features of nonlinear differential equations cannot be adequately represented by finite-difference method and vice versa.

  3. Direct approach for solving nonlinear evolution and two-point

    Indian Academy of Sciences (India)

    Time-delayed nonlinear evolution equations and boundary value problems have a wide range of applications in science and engineering. In this paper, we implement the differential transform method to solve the nonlinear delay differential equation and boundary value problems. Also, we present some numerical examples ...

  4. Multiobjective Two-Stage Stochastic Programming Problems with Interval Discrete Random Variables

    Directory of Open Access Journals (Sweden)

    S. K. Barik

    2012-01-01

    Full Text Available Most of the real-life decision-making problems have more than one conflicting and incommensurable objective functions. In this paper, we present a multiobjective two-stage stochastic linear programming problem considering some parameters of the linear constraints as interval type discrete random variables with known probability distribution. Randomness of the discrete intervals are considered for the model parameters. Further, the concepts of best optimum and worst optimum solution are analyzed in two-stage stochastic programming. To solve the stated problem, first we remove the randomness of the problem and formulate an equivalent deterministic linear programming model with multiobjective interval coefficients. Then the deterministic multiobjective model is solved using weighting method, where we apply the solution procedure of interval linear programming technique. We obtain the upper and lower bound of the objective function as the best and the worst value, respectively. It highlights the possible risk involved in the decision-making tool. A numerical example is presented to demonstrate the proposed solution procedure.

  5. Generalized Benders’ Decomposition for topology optimization problems

    DEFF Research Database (Denmark)

    Munoz Queupumil, Eduardo Javier; Stolpe, Mathias

    2011-01-01

    ) problems with discrete design variables to global optimality. We present the theoretical aspects of the method, including a proof of finite convergence and conditions for obtaining global optimal solutions. The method is also linked to, and compared with, an Outer-Approximation approach and a mixed 0......–1 semi definite programming formulation of the considered problem. Several ways to accelerate the method are suggested and an implementation is described. Finally, a set of truss topology optimization problems are numerically solved to global optimality.......This article considers the non-linear mixed 0–1 optimization problems that appear in topology optimization of load carrying structures. The main objective is to present a Generalized Benders’ Decomposition (GBD) method for solving single and multiple load minimum compliance (maximum stiffness...

  6. Uncertainty Quantification and Bifurcation Analysis of an Airfoil with Multiple Nonlinearities

    Directory of Open Access Journals (Sweden)

    Haitao Liao

    2013-01-01

    Full Text Available In order to calculate the limit cycle oscillations and bifurcations of nonlinear aeroelastic system, the problem of finding periodic solutions with maximum vibration amplitude is transformed into a nonlinear optimization problem. An algebraic system of equations obtained by the harmonic balance method and the stability condition derived from the Floquet theory are used to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated, and the effects of structural parameter uncertainty on the limit cycle oscillations and bifurcations of an airfoil with multiple nonlinearities are studied. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.

  7. Program evaluation and incentives for administrators of energy-efficiency programs: Can evaluation solve the principal/agent problem?

    Energy Technology Data Exchange (ETDEWEB)

    Blumstein, Carl, E-mail: blumstei@berkeley.ed [University of California Energy Institute, 2547 Channing Way, Berkeley, CA 94720 (United States)

    2010-10-15

    This paper addresses the nexus between evaluation of energy-efficiency programs and incentive payments based on performance for program administrators in California. The paper describes the problems that arise when evaluators are asked to measure program performance by answering the counterfactual question-what would have happened in the absence of the program? Then the paper examines some ways of addressing these problems. Key conclusions are (1) program evaluation cannot precisely and accurately determine the counterfactual, there will always be substantial uncertainty, (2) given the current state of knowledge, the decision to tie all incentives to program outcomes is misguided, and (3) incentive programs should be regularly reviewed and revised so that they can be adapted to new conditions.

  8. Program evaluation and incentives for administrators of energy-efficiency programs. Can evaluation solve the principal/agent problem?

    Energy Technology Data Exchange (ETDEWEB)

    Blumstein, Carl [University of California Energy Institute, 2547 Channing Way, Berkeley, CA 94720 (United States)

    2010-10-15

    This paper addresses the nexus between evaluation of energy-efficiency programs and incentive payments based on performance for program administrators in California. The paper describes the problems that arise when evaluators are asked to measure program performance by answering the counterfactual question - what would have happened in the absence of the program? Then the paper examines some ways of addressing these problems. Key conclusions are (1) program evaluation cannot precisely and accurately determine the counterfactual, there will always be substantial uncertainty, (2) given the current state of knowledge, the decision to tie all incentives to program outcomes is misguided, and (3) incentive programs should be regularly reviewed and revised so that they can be adapted to new conditions. (author)

  9. Program evaluation and incentives for administrators of energy-efficiency programs: Can evaluation solve the principal/agent problem?

    International Nuclear Information System (INIS)

    Blumstein, Carl

    2010-01-01

    This paper addresses the nexus between evaluation of energy-efficiency programs and incentive payments based on performance for program administrators in California. The paper describes the problems that arise when evaluators are asked to measure program performance by answering the counterfactual question-what would have happened in the absence of the program? Then the paper examines some ways of addressing these problems. Key conclusions are (1) program evaluation cannot precisely and accurately determine the counterfactual, there will always be substantial uncertainty, (2) given the current state of knowledge, the decision to tie all incentives to program outcomes is misguided, and (3) incentive programs should be regularly reviewed and revised so that they can be adapted to new conditions.

  10. A non-linear branch and cut method for solving discrete minimum compliance problems to global optimality

    DEFF Research Database (Denmark)

    Stolpe, Mathias; Bendsøe, Martin P.

    2007-01-01

    This paper present some initial results pertaining to a search for globally optimal solutions to a challenging benchmark example proposed by Zhou and Rozvany. This means that we are dealing with global optimization of the classical single load minimum compliance topology design problem with a fixed...... finite element discretization and with discrete design variables. Global optimality is achieved by the implementation of some specially constructed convergent nonlinear branch and cut methods, based on the use of natural relaxations and by applying strengthening constraints (linear valid inequalities......) and cuts....

  11. Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings.

    Science.gov (United States)

    Tang, Yang; Gao, Huijun; Zou, Wei; Kurths, Jürgen

    2013-02-01

    In this paper, the distributed synchronization problem of networks of agent systems with controllers and nonlinearities subject to Bernoulli switchings is investigated. Controllers and adaptive updating laws injected in each vertex of networks depend on the state information of its neighborhood. Three sets of Bernoulli stochastic variables are introduced to describe the occurrence probabilities of distributed adaptive controllers, updating laws and nonlinearities, respectively. By the Lyapunov functions method, we show that the distributed synchronization of networks composed of agent systems with multiple randomly occurring nonlinearities, multiple randomly occurring controllers, and multiple randomly occurring updating laws can be achieved in mean square under certain criteria. The conditions derived in this paper can be solved by semi-definite programming. Moreover, by mathematical analysis, we find that the coupling strength, the probabilities of the Bernoulli stochastic variables, and the form of nonlinearities have great impacts on the convergence speed and the terminal control strength. The synchronization criteria and the observed phenomena are demonstrated by several numerical simulation examples. In addition, the advantage of distributed adaptive controllers over conventional adaptive controllers is illustrated.

  12. Memetic Algorithms to Solve a Global Nonlinear Optimization Problem. A Review

    Directory of Open Access Journals (Sweden)

    M. K. Sakharov

    2015-01-01

    Full Text Available In recent decades, evolutionary algorithms have proven themselves as the powerful optimization techniques of search engine. Their popularity is due to the fact that they are easy to implement and can be used in all areas, since they are based on the idea of universal evolution. For example, in the problems of a large number of local optima, the traditional optimization methods, usually, fail in finding the global optimum. To solve such problems using a variety of stochastic methods, in particular, the so-called population-based algorithms, which are a kind of evolutionary methods. The main disadvantage of this class of methods is their slow convergence to the exact solution in the neighborhood of the global optimum, as these methods incapable to use the local information about the landscape of the function. This often limits their use in largescale real-world problems where the computation time is a critical factor.One of the promising directions in the field of modern evolutionary computation are memetic algorithms, which can be regarded as a combination of population search of the global optimum and local procedures for verifying solutions, which gives a synergistic effect. In the context of memetic algorithms, the meme is an implementation of the local optimization method to refine solution in the search.The concept of memetic algorithms provides ample opportunities for the development of various modifications of these algorithms, which can vary the frequency of the local search, the conditions of its end, and so on. The practically significant memetic algorithm modifications involve the simultaneous use of different memes. Such algorithms are called multi-memetic.The paper gives statement of the global problem of nonlinear unconstrained optimization, describes the most promising areas of AI modifications, including hybridization and metaoptimization. The main content of the work is the classification and review of existing varieties of

  13. Polymorphic Uncertain Linear Programming for Generalized Production Planning Problems

    Directory of Open Access Journals (Sweden)

    Xinbo Zhang

    2014-01-01

    Full Text Available A polymorphic uncertain linear programming (PULP model is constructed to formulate a class of generalized production planning problems. In accordance with the practical environment, some factors such as the consumption of raw material, the limitation of resource and the demand of product are incorporated into the model as parameters of interval and fuzzy subsets, respectively. Based on the theory of fuzzy interval program and the modified possibility degree for the order of interval numbers, a deterministic equivalent formulation for this model is derived such that a robust solution for the uncertain optimization problem is obtained. Case study indicates that the constructed model and the proposed solution are useful to search for an optimal production plan for the polymorphic uncertain generalized production planning problems.

  14. Semiclassical soliton ensembles for the focusing nonlinear Schrödinger equation

    CERN Document Server

    Kamvissis, Spyridon; Miller, Peter D

    2003-01-01

    This book represents the first asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrödinger equation in the semiclassical asymptotic regime. This problem is a key model in nonlinear optical physics and has increasingly important applications in the telecommunications industry. The authors exploit complete integrability to establish pointwise asymptotics for this problem's solution in the semiclassical regime and explicit integration for the underlying nonlinear, elliptic, partial differential equations suspected of governing

  15. Nonlinear acceleration of SN transport calculations

    Energy Technology Data Exchange (ETDEWEB)

    Fichtl, Erin D [Los Alamos National Laboratory; Warsa, James S [Los Alamos National Laboratory; Calef, Matthew T [Los Alamos National Laboratory

    2010-12-20

    The use of nonlinear iterative methods, Jacobian-Free Newton-Krylov (JFNK) in particular, for solving eigenvalue problems in transport applications has recently become an active subject of research. While JFNK has been shown to be effective for k-eigenvalue problems, there are a number of input parameters that impact computational efficiency, making it difficult to implement efficiently in a production code using a single set of default parameters. We show that different selections for the forcing parameter in particular can lead to large variations in the amount of computational work for a given problem. In contrast, we present a nonlinear subspace method that sits outside and effectively accelerates nonlinear iterations of a given form and requires only a single input parameter, the subspace size. It is shown to consistently and significantly reduce the amount of computational work when applied to fixed-point iteration, and this combination of methods is shown to be more efficient than JFNK for our application.

  16. Stabilization of nonlinear excitations by disorder

    DEFF Research Database (Denmark)

    Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Johansson, M.

    1998-01-01

    Using analytical and numerical techniques we analyze the static and dynamical properties of solitonlike excitations in the presence of parametric disorder in the one-dimensional nonlinear Schrodinger equation with a homogeneous power nonlinearity. Both the continuum and the discrete problem...... are investigated. We find that otherwise unstable excitations can be stabilized by the presence of disorder in the continuum problem. For the very narrow excitations of the discrete problem we find that the disorder has no effect on the averaged behavior. Finally, we show that the disorder can be applied to induce...... a high degree of controllability of the spatial extent of the stable excitations in the continuum system....

  17. Path selection and bandwidth allocation in MPLS networks: a nonlinear programming approach

    Science.gov (United States)

    Burns, J. E.; Ott, Teunis J.; de Kock, Johan M.; Krzesinski, Anthony E.

    2001-07-01

    Multi-protocol Label Switching extends the IPv4 destination-based routing protocols to provide new and scalable routing capabilities in connectionless networks using relatively simple packet forwarding mechanisms. MPLS networks carry traffic on virtual connections called label switched paths. This paper considers path selection and bandwidth allocation in MPLS networks in order to optimize the network quality of service. The optimization is based upon the minimization of a non-linear objective function which under light load simplifies to OSPF routing with link metrics equal to the link propagation delays. The behavior under heavy load depends on the choice of certain parameters: It can essentially be made to minimize maximal expected utilization, or to maximize minimal expected weighted slacks (both over all links). Under certain circumstances it can be made to minimize the probability that a link has an instantaneous offered load larger than its transmission capacity. We present a model of an MPLS network and an algorithm to find and capacitate optimal LSPs. The algorithm is an improvement of the well-known flow deviation non-linear programming method. The algorithm is applied to compute optimal LSPs for several test networks carrying a single traffic class.

  18. Nonlinear finite element analyses: advances and challenges in dental applications.

    Science.gov (United States)

    Wakabayashi, N; Ona, M; Suzuki, T; Igarashi, Y

    2008-07-01

    To discuss the development and current status of application of nonlinear finite element method (FEM) in dentistry. The literature was searched for original research articles with keywords such as nonlinear, finite element analysis, and tooth/dental/implant. References were selected manually or searched from the PUBMED and MEDLINE databases through November 2007. The nonlinear problems analyzed in FEM studies were reviewed and categorized into: (A) nonlinear simulations of the periodontal ligament (PDL), (B) plastic and viscoelastic behaviors of dental materials, (C) contact phenomena in tooth-to-tooth contact, (D) contact phenomena within prosthodontic structures, and (E) interfacial mechanics between the tooth and the restoration. The FEM in dentistry recently focused on simulation of realistic intra-oral conditions such as the nonlinear stress-strain relationship in the periodontal tissues and the contact phenomena in teeth, which could hardly be solved by the linear static model. The definition of contact area critically affects the reliability of the contact analyses, especially for implant-abutment complexes. To predict the failure risk of a bonded tooth-restoration interface, it is essential to assess the normal and shear stresses relative to the interface. The inclusion of viscoelasticity and plastic deformation to the program to account for the time-dependent, thermal sensitive, and largely deformable nature of dental materials would enhance its application. Further improvement of the nonlinear FEM solutions should be encouraged to widen the range of applications in dental and oral health science.

  19. SPARSE ELECTROMAGNETIC IMAGING USING NONLINEAR LANDWEBER ITERATIONS

    KAUST Repository

    Desmal, Abdulla; Bagci, Hakan

    2015-01-01

    minimization problem is solved using nonlinear Landweber iterations, where at each iteration a thresholding function is applied to enforce the sparseness-promoting L0/L1-norm constraint. The thresholded nonlinear Landweber iterations are applied to several two

  20. Program evaluation and incentives for administrators of energy efficiency programs: can evaluation solve the principal/agent problem?

    Energy Technology Data Exchange (ETDEWEB)

    Blumstein, Carl (Univ. of California, Energy Institute (United States))

    2009-07-01

    This paper addresses the nexus between the evaluation of energy-efficiency programs and incentive payments based on performance for program administrators in California. The paper describes problems that arise when evaluators are asked to measure program performance by answering the counterfactual question, what would have happened in the absence of the program? Then some ways of addressing these problems are examined. Key conclusions are that 1) program evaluation cannot precisely and accurately determine the counterfactual, there will always be substantial uncertainty, 2) given the current state of knowledge, the decision to tie all of the incentive to program outcomes is misguided, and 3) incentive programs should be regularly reviewed and revised so that they can be adapted to new conditions.

  1. Problem area descriptions : motor vehicle crashes - data analysis and IVI program analysis

    Science.gov (United States)

    In general, the IVI program focuses on the more significant safety problem categories as : indicated by statistical analyses of crash data. However, other factors were considered in setting : program priorities and schedules. For some problem areas, ...

  2. Portfolios with nonlinear constraints and spin glasses

    Science.gov (United States)

    Gábor, Adrienn; Kondor, I.

    1999-12-01

    In a recent paper Galluccio, Bouchaud and Potters demonstrated that a certain portfolio problem with a nonlinear constraint maps exactly onto finding the ground states of a long-range spin glass, with the concomitant nonuniqueness and instability of the optimal portfolios. Here we put forward geometric arguments that lead to qualitatively similar conclusions, without recourse to the methods of spin glass theory, and give two more examples of portfolio problems with convex nonlinear constraints.

  3. Interactive Fuzzy Goal Programming approach in multi-response stratified sample surveys

    Directory of Open Access Journals (Sweden)

    Gupta Neha

    2016-01-01

    Full Text Available In this paper, we applied an Interactive Fuzzy Goal Programming (IFGP approach with linear, exponential and hyperbolic membership functions, which focuses on maximizing the minimum membership values to determine the preferred compromise solution for the multi-response stratified surveys problem, formulated as a Multi- Objective Non Linear Programming Problem (MONLPP, and by linearizing the nonlinear objective functions at their individual optimum solution, the problem is approximated to an Integer Linear Programming Problem (ILPP. A numerical example based on real data is given, and comparison with some existing allocations viz. Cochran’s compromise allocation, Chatterjee’s compromise allocation and Khowaja’s compromise allocation is made to demonstrate the utility of the approach.

  4. Analytical treatment of the nonlinear electron cloud effect and the combined effects with beam-beam and space charge nonlinear forces in storage rings

    International Nuclear Information System (INIS)

    Gao Jie

    2009-01-01

    In this paper we treat first some nonlinear beam dynamics problems in storage rings, such as beam dynamic apertures due to magnetic multipoles, wiggles, beam-beam effects, nonlinear space charge effect, and then nonlinear electron cloud effect combined with beam-beam and space charge effects, analytically. This analytical treatment is applied to BEPC II. The corresponding analytical expressions developed in this paper are useful both in understanding the physics behind these problems and also in making practical quick hand estimations. (author)

  5. A Hybrid Programming Framework for Modeling and Solving Constraint Satisfaction and Optimization Problems

    OpenAIRE

    Sitek, Paweł; Wikarek, Jarosław

    2016-01-01

    This paper proposes a hybrid programming framework for modeling and solving of constraint satisfaction problems (CSPs) and constraint optimization problems (COPs). Two paradigms, CLP (constraint logic programming) and MP (mathematical programming), are integrated in the framework. The integration is supplemented with the original method of problem transformation, used in the framework as a presolving method. The transformation substantially reduces the feasible solution space. The framework a...

  6. International Conference on Applications in Nonlinear Dynamics

    CERN Document Server

    Longhini, Patrick; Palacios, Antonio

    2017-01-01

    This book presents collaborative research works carried out by experimentalists and theorists around the world in the field of nonlinear dynamical systems. It provides a forum for applications of nonlinear systems while solving practical problems in science and engineering. Topics include: Applied Nonlinear Optics, Sensor, Radar & Communication Signal Processing, Nano Devices, Nonlinear Biomedical Applications, Circuits & Systems, Coupled Nonlinear Oscillator, Precision Timing Devices, Networks, and other contemporary topics in the general field of Nonlinear Science. This book provides a comprehensive report of the various research projects presented at the International Conference on Applications in Nonlinear Dynamics (ICAND 2016) held in Denver, Colorado, 2016. It can be a valuable tool for scientists and engineering interested in connecting ideas and methods in nonlinear dynamics with actual design, fabrication and implementation of engineering applications or devices.

  7. Neural-network-observer-based optimal control for unknown nonlinear systems using adaptive dynamic programming

    Science.gov (United States)

    Liu, Derong; Huang, Yuzhu; Wang, Ding; Wei, Qinglai

    2013-09-01

    In this paper, an observer-based optimal control scheme is developed for unknown nonlinear systems using adaptive dynamic programming (ADP) algorithm. First, a neural-network (NN) observer is designed to estimate system states. Then, based on the observed states, a neuro-controller is constructed via ADP method to obtain the optimal control. In this design, two NN structures are used: a three-layer NN is used to construct the observer which can be applied to systems with higher degrees of nonlinearity and without a priori knowledge of system dynamics, and a critic NN is employed to approximate the value function. The optimal control law is computed using the critic NN and the observer NN. Uniform ultimate boundedness of the closed-loop system is guaranteed. The actor, critic, and observer structures are all implemented in real-time, continuously and simultaneously. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

  8. Problem Space Matters: Evaluation of a German Enrichment Program for Gifted Children.

    Science.gov (United States)

    Welter, Marisete M; Jaarsveld, Saskia; Lachmann, Thomas

    2018-01-01

    We studied the development of cognitive abilities related to intelligence and creativity ( N = 48, 6-10 years old), using a longitudinal design (over one school year), in order to evaluate an Enrichment Program for gifted primary school children initiated by the government of the German federal state of Rhineland-Palatinate ( Entdeckertag Rheinland Pfalz , Germany; ET; Day of Discoverers). A group of German primary school children ( N = 24), identified earlier as intellectually gifted and selected to join the ET program was compared to a gender-, class- and IQ- matched group of control children that did not participate in this program. All participants performed the Standard Progressive Matrices (SPM) test, which measures intelligence in well-defined problem space; the Creative Reasoning Task (CRT), which measures intelligence in ill-defined problem space; and the test of creative thinking-drawing production (TCT-DP), which measures creativity, also in ill-defined problem space. Results revealed that problem space matters: the ET program is effective only for the improvement of intelligence operating in well-defined problem space. An effect was found for intelligence as measured by SPM only, but neither for intelligence operating in ill-defined problem space (CRT) nor for creativity (TCT-DP). This suggests that, depending on the type of problem spaces presented, different cognitive abilities are elicited in the same child. Therefore, enrichment programs for gifted, but also for children attending traditional schools, should provide opportunities to develop cognitive abilities related to intelligence, operating in both well- and ill-defined problem spaces, and to creativity in a parallel, using an interactive approach.

  9. Generalized Nash equilibrium problems, bilevel programming and mpec

    CERN Document Server

    Lalitha, CS

    2017-01-01

    The book discusses three classes of problems: the generalized Nash equilibrium problems, the bilevel problems and the mathematical programming with equilibrium constraints (MPEC). These problems interact through their mathematical analysis as well as their applications. The primary aim of the book is to present the modern tool of variational analysis and optimization, which are used to analyze these three classes of problems. All contributing authors are respected academicians, scientists and researchers from around the globe. These contributions are based on the lectures delivered by experts at CIMPA School, held at the University of Delhi, India, from 25 November–6 December 2013, and peer-reviewed by international experts. The book contains five chapters. Chapter 1 deals with nonsmooth, nonconvex bilevel optimization problems whose feasible set is described by using the graph of the solution set mapping of a parametric optimization problem. Chapter 2 describes a constraint qualification to MPECs considere...

  10. Non-linear dynamic response of reactor containment

    International Nuclear Information System (INIS)

    Takemori, T.; Sotomura, K.; Yamada, M.

    1975-01-01

    A computer program was developed to investigate the elasto-plastic behavior of structures. This program is outlined and the problems of non-linear response of structures are discussed. Since the mode superposition method is only valid in an elastic analysis, the direct integration method was adopted here. As the sample model, an actual reactor containment (reactor building) of PWR plant was adopted. This building consists of three components, that is, a concrete internal structure, a steel containment vessel and a concrete outer shield wall. These components are resting on a rigid foundation mat. Therefore they were modeled with a lumped mass model respectively and coupled on the foundation. The following assumptions were employed to establish the properties of dynamic model: rocking and swaying springs of soil can be obtained from an elastic half-space solution, and the hysteretic characteristic of springs is bi-linear; springs connecting each mass are dealt with shear beams so that both bending and shear deflections can be included (Hysteretic characteristics of springs are linear, bi-linear and tri-linear for the internal structure, the containment vessel and the outer shield wall, respectively); generally, each damping coefficient is given for each mode in modal superposition (However, a damping matrix must be made directly in a non-linear response). Therefore the damping matrix of the model was made by combining the damping matrices [C] of each component obtained by Caughy's method and a damping value of the rocking and swaying by the half-space solution. On the basis of above conditions, the non-linear response of the structure was obtained and the difference between elastic and elasto-plastic analysis is presented

  11. Existence and discrete approximation for optimization problems governed by fractional differential equations

    Science.gov (United States)

    Bai, Yunru; Baleanu, Dumitru; Wu, Guo-Cheng

    2018-06-01

    We investigate a class of generalized differential optimization problems driven by the Caputo derivative. Existence of weak Carathe ´odory solution is proved by using Weierstrass existence theorem, fixed point theorem and Filippov implicit function lemma etc. Then a numerical approximation algorithm is introduced, and a convergence theorem is established. Finally, a nonlinear programming problem constrained by the fractional differential equation is illustrated and the results verify the validity of the algorithm.

  12. Sensitivity analysis of linear programming problem through a recurrent neural network

    Science.gov (United States)

    Das, Raja

    2017-11-01

    In this paper we study the recurrent neural network for solving linear programming problems. To achieve optimality in accuracy and also in computational effort, an algorithm is presented. We investigate the sensitivity analysis of linear programming problem through the neural network. A detailed example is also presented to demonstrate the performance of the recurrent neural network.

  13. Efficient decomposition and linearization methods for the stochastic transportation problem

    International Nuclear Information System (INIS)

    Holmberg, K.

    1993-01-01

    The stochastic transportation problem can be formulated as a convex transportation problem with nonlinear objective function and linear constraints. We compare several different methods based on decomposition techniques and linearization techniques for this problem, trying to find the most efficient method or combination of methods. We discuss and test a separable programming approach, the Frank-Wolfe method with and without modifications, the new technique of mean value cross decomposition and the more well known Lagrangian relaxation with subgradient optimization, as well as combinations of these approaches. Computational tests are presented, indicating that some new combination methods are quite efficient for large scale problems. (authors) (27 refs.)

  14. Probabilistic finite elements for transient analysis in nonlinear continua

    Science.gov (United States)

    Liu, W. K.; Belytschko, T.; Mani, A.

    1985-01-01

    The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.

  15. Topology optimization of Channel flow problems

    DEFF Research Database (Denmark)

    Gersborg-Hansen, Allan; Sigmund, Ole; Haber, R. B.

    2005-01-01

    function which measures either some local aspect of the velocity field or a global quantity, such as the rate of energy dissipation. We use the finite element method to model the flow, and we solve the optimization problem with a gradient-based math-programming algorithm that is driven by analytical......This paper describes a topology design method for simple two-dimensional flow problems. We consider steady, incompressible laminar viscous flows at low to moderate Reynolds numbers. This makes the flow problem non-linear and hence a non-trivial extension of the work of [Borrvall&Petersson 2002......]. Further, the inclusion of inertia effects significantly alters the physics, enabling solutions of new classes of optimization problems, such as velocity--driven switches, that are not addressed by the earlier method. Specifically, we determine optimal layouts of channel flows that extremize a cost...

  16. Dynamic Programming Approaches for the Traveling Salesman Problem with Drone

    OpenAIRE

    Bouman, Paul; Agatz, Niels; Schmidt, Marie

    2017-01-01

    markdownabstractA promising new delivery model involves the use of a delivery truck that collaborates with a drone to make deliveries. Effectively combining a drone and a truck gives rise to a new planning problem that is known as the Traveling Salesman Problem with Drone (TSP-D). This paper presents an exact solution approach for the TSP-D based on dynamic programming and present experimental results of different dynamic programming based heuristics. Our numerical experiments show that our a...

  17. High-precision numerical simulation with autoadaptative grid technique in nonlinear thermal diffusion

    International Nuclear Information System (INIS)

    Chambarel, A.; Pumborios, M.

    1992-01-01

    This paper reports that many engineering problems concern the determination of a steady state solution in the case with strong thermal gradients, and results obtained using the finite-element technique are sometimes inaccurate, particularly for nonlinear problems with unadapted meshes. Building on previous results in linear problems, we propose an autoadaptive technique for nonlinear cases that uses quasi-Newtonian iterations to reevaluate an interpolation error estimation. The authors perfected an automatic refinement technique to solve the nonlinear thermal problem of temperature calculus in a cast-iron cylinder head of a diesel engine

  18. Domain decomposition solvers for nonlinear multiharmonic finite element equations

    KAUST Repository

    Copeland, D. M.

    2010-01-01

    In many practical applications, for instance, in computational electromagnetics, the excitation is time-harmonic. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple elliptic equation for the amplitude. This is true for linear problems, but not for nonlinear problems. However, due to the periodicity of the solution, we can expand the solution in a Fourier series. Truncating this Fourier series and approximating the Fourier coefficients by finite elements, we arrive at a large-scale coupled nonlinear system for determining the finite element approximation to the Fourier coefficients. The construction of fast solvers for such systems is very crucial for the efficiency of this multiharmonic approach. In this paper we look at nonlinear, time-harmonic potential problems as simple model problems. We construct and analyze almost optimal solvers for the Jacobi systems arising from the Newton linearization of the large-scale coupled nonlinear system that one has to solve instead of performing the expensive time-integration procedure. © 2010 de Gruyter.

  19. Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem

    Science.gov (United States)

    Chen, Wei

    2015-07-01

    In this paper, we discuss the portfolio optimization problem with real-world constraints under the assumption that the returns of risky assets are fuzzy numbers. A new possibilistic mean-semiabsolute deviation model is proposed, in which transaction costs, cardinality and quantity constraints are considered. Due to such constraints the proposed model becomes a mixed integer nonlinear programming problem and traditional optimization methods fail to find the optimal solution efficiently. Thus, a modified artificial bee colony (MABC) algorithm is developed to solve the corresponding optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm.

  20. Nonlinear Electron Waves in Strongly Magnetized Plasmas

    DEFF Research Database (Denmark)

    Pécseli, Hans; Juul Rasmussen, Jens

    1980-01-01

    Weakly nonlinear dispersive electron waves in strongly magnetized plasma are considered. A modified nonlinear Schrodinger equation is derived taking into account the effect of particles resonating with the group velocity of the waves (nonlinear Landau damping). The possibility of including the ion...... dynamics in the analysis is also demonstrated. As a particular case the authors investigate nonlinear waves in a strongly magnetized plasma filled wave-guide, where the effects of finite geometry are important. The relevance of this problem to laboratory experiments is discussed....