Linear programming using Matlab

CERN Document Server

Ploskas, Nikolaos

2017-01-01

This book offers a theoretical and computational presentation of a variety of linear programming algorithms and methods with an emphasis on the revised simplex method and its components. A theoretical background and mathematical formulation is included for each algorithm as well as comprehensive numerical examples and corresponding MATLAB® code. The MATLAB® implementations presented in this book  are sophisticated and allow users to find solutions to large-scale benchmark linear programs. Each algorithm is followed by a computational study on benchmark problems that analyze the computational behavior of the presented algorithms. As a solid companion to existing algorithmic-specific literature, this book will be useful to researchers, scientists, mathematical programmers, and students with a basic knowledge of linear algebra and calculus.  The clear presentation enables the reader to understand and utilize all components of simplex-type methods, such as presolve techniques, scaling techniques, pivoting ru...

Analysis of the efficiency of the linearization techniques for solving multi-objective linear fractional programming problems by goal programming

Directory of Open Access Journals (Sweden)

Tunjo Perić

2017-01-01

Full Text Available This paper presents and analyzes the applicability of three linearization techniques used for solving multi-objective linear fractional programming problems using the goal programming method. The three linearization techniques are: (1 Taylor’s polynomial linearization approximation, (2 the method of variable change, and (3 a modification of the method of variable change proposed in [20]. All three linearization techniques are presented and analyzed in two variants: (a using the optimal value of the objective functions as the decision makers’ aspirations, and (b the decision makers’ aspirations are given by the decision makers. As the criteria for the analysis we use the efficiency of the obtained solutions and the difficulties the analyst comes upon in preparing the linearization models. To analyze the applicability of the linearization techniques incorporated in the linear goal programming method we use an example of a financial structure optimization problem.

175 Years of Linear Programming

Indian Academy of Sciences (India)

polynomial-time solvability of linear programming, that is, testing if a polyhedron Q E ~ ... Q is rational, i.e. all extreme points and rays of Q are ra- tional vectors or ..... rithrll terminates with an interior solution, a post-processing step is usually ...

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.

Portfolio optimization using fuzzy linear programming

Science.gov (United States)

Pandit, Purnima K.

2013-09-01

Portfolio Optimization (PO) is a problem in Finance, in which investor tries to maximize return and minimize risk by carefully choosing different assets. Expected return and risk are the most important parameters with regard to optimal portfolios. In the simple form PO can be modeled as quadratic programming problem which can be put into equivalent linear form. PO problems with the fuzzy parameters can be solved as multi-objective fuzzy linear programming problem. In this paper we give the solution to such problems with an illustrative example.

Linear superposition solutions to nonlinear wave equations

International Nuclear Information System (INIS)

Liu Yu

2012-01-01

The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed

Solution of a General Linear Complementarity Problem Using Smooth Optimization and Its Application to Bilinear Programming and LCP

International Nuclear Information System (INIS)

Fernandes, L.; Friedlander, A.; Guedes, M.; Judice, J.

2001-01-01

This paper addresses a General Linear Complementarity Problem (GLCP) that has found applications in global optimization. It is shown that a solution of the GLCP can be computed by finding a stationary point of a differentiable function over a set defined by simple bounds on the variables. The application of this result to the solution of bilinear programs and LCPs is discussed. Some computational evidence of its usefulness is included in the last part of the paper

Linear programming mathematics, theory and algorithms

CERN Document Server

1996-01-01

Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory. Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming.

No-signaling quantum key distribution: solution by linear programming

Science.gov (United States)

Hwang, Won-Young; Bae, Joonwoo; Killoran, Nathan

2015-02-01

We outline a straightforward approach for obtaining a secret key rate using only no-signaling constraints and linear programming. Assuming an individual attack, we consider all possible joint probabilities. Initially, we study only the case where Eve has binary outcomes, and we impose constraints due to the no-signaling principle and given measurement outcomes. Within the remaining space of joint probabilities, by using linear programming, we get bound on the probability of Eve correctly guessing Bob's bit. We then make use of an inequality that relates this guessing probability to the mutual information between Bob and a more general Eve, who is not binary-restricted. Putting our computed bound together with the Csiszár-Körner formula, we obtain a positive key generation rate. The optimal value of this rate agrees with known results, but was calculated in a more straightforward way, offering the potential of generalization to different scenarios.

Computer programs for the solution of systems of linear algebraic equations

Science.gov (United States)

Sequi, W. T.

1973-01-01

FORTRAN subprograms for the solution of systems of linear algebraic equations are described, listed, and evaluated in this report. Procedures considered are direct solution, iteration, and matrix inversion. Both incore methods and those which utilize auxiliary data storage devices are considered. Some of the subroutines evaluated require the entire coefficient matrix to be in core, whereas others account for banding or sparceness of the system. General recommendations relative to equation solving are made, and on the basis of tests, specific subprograms are recommended.

Reduction of Linear Programming to Linear Approximation

OpenAIRE

Vaserstein, Leonid N.

2006-01-01

It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.

FSILP: fuzzy-stochastic-interval linear programming for supporting municipal solid waste management.

Science.gov (United States)

Li, Pu; Chen, Bing

2011-04-01

Although many studies on municipal solid waste management (MSW management) were conducted under uncertain conditions of fuzzy, stochastic, and interval coexistence, the solution to the conventional linear programming problems of integrating fuzzy method with the other two was inefficient. In this study, a fuzzy-stochastic-interval linear programming (FSILP) method is developed by integrating Nguyen's method with conventional linear programming for supporting municipal solid waste management. The Nguyen's method was used to convert the fuzzy and fuzzy-stochastic linear programming problems into the conventional linear programs, by measuring the attainment values of fuzzy numbers and/or fuzzy random variables, as well as superiority and inferiority between triangular fuzzy numbers/triangular fuzzy-stochastic variables. The developed method can effectively tackle uncertainties described in terms of probability density functions, fuzzy membership functions, and discrete intervals. Moreover, the method can also improve upon the conventional interval fuzzy programming and two-stage stochastic programming approaches, with advantageous capabilities that are easily achieved with fewer constraints and significantly reduces consumption time. The developed model was applied to a case study of municipal solid waste management system in a city. The results indicated that reasonable solutions had been generated. The solution can help quantify the relationship between the change of system cost and the uncertainties, which could support further analysis of tradeoffs between the waste management cost and the system failure risk. Copyright © 2010 Elsevier Ltd. All rights reserved.

ALPS - A LINEAR PROGRAM SOLVER

Science.gov (United States)

Viterna, L. A.

1994-01-01

Linear programming is a widely-used engineering and management tool. Scheduling, resource allocation, and production planning are all well-known applications of linear programs (LP's). Most LP's are too large to be solved by hand, so over the decades many computer codes for solving LP's have been developed. ALPS, A Linear Program Solver, is a full-featured LP analysis program. ALPS can solve plain linear programs as well as more complicated mixed integer and pure integer programs. ALPS also contains an efficient solution technique for pure binary (0-1 integer) programs. One of the many weaknesses of LP solvers is the lack of interaction with the user. ALPS is a menu-driven program with no special commands or keywords to learn. In addition, ALPS contains a full-screen editor to enter and maintain the LP formulation. These formulations can be written to and read from plain ASCII files for portability. For those less experienced in LP formulation, ALPS contains a problem "parser" which checks the formulation for errors. ALPS creates fully formatted, readable reports that can be sent to a printer or output file. ALPS is written entirely in IBM's APL2/PC product, Version 1.01. The APL2 workspace containing all the ALPS code can be run on any APL2/PC system (AT or 386). On a 32-bit system, this configuration can take advantage of all extended memory. The user can also examine and modify the ALPS code. The APL2 workspace has also been "packed" to be run on any DOS system (without APL2) as a stand-alone "EXE" file, but has limited memory capacity on a 640K system. A numeric coprocessor (80X87) is optional but recommended. The standard distribution medium for ALPS is a 5.25 inch 360K MS-DOS format diskette. IBM, IBM PC and IBM APL2 are registered trademarks of International Business Machines Corporation. MS-DOS is a registered trademark of Microsoft Corporation.

Some Properties of Multiple Parameters Linear Programming

Directory of Open Access Journals (Sweden)

Maoqin Li

2010-01-01

Full Text Available We consider a linear programming problem in which the right-hand side vector depends on multiple parameters. We study the characters of the optimal value function and the critical regions based on the concept of the optimal partition. We show that the domain of the optimal value function f can be decomposed into finitely many subsets with disjoint relative interiors, which is different from the result based on the concept of the optimal basis. And any directional derivative of f at any point can be computed by solving a linear programming problem when only an optimal solution is available at the point.

Some Properties of Multiple Parameters Linear Programming

Directory of Open Access Journals (Sweden)

Yan Hong

2010-01-01

Full Text Available Abstract We consider a linear programming problem in which the right-hand side vector depends on multiple parameters. We study the characters of the optimal value function and the critical regions based on the concept of the optimal partition. We show that the domain of the optimal value function can be decomposed into finitely many subsets with disjoint relative interiors, which is different from the result based on the concept of the optimal basis. And any directional derivative of at any point can be computed by solving a linear programming problem when only an optimal solution is available at the point.

SLAP, Large Sparse Linear System Solution Package

International Nuclear Information System (INIS)

Greenbaum, A.

1987-01-01

1 - Description of program or function: SLAP is a set of routines for solving large sparse systems of linear equations. One need not store the entire matrix - only the nonzero elements and their row and column numbers. Any nonzero structure is acceptable, so the linear system solver need not be modified when the structure of the matrix changes. Auxiliary storage space is acquired and released within the routines themselves by use of the LRLTRAN POINTER statement. 2 - Method of solution: SLAP contains one direct solver, a band matrix factorization and solution routine, BAND, and several interactive solvers. The iterative routines are as follows: JACOBI, Jacobi iteration; GS, Gauss-Seidel Iteration; ILUIR, incomplete LU decomposition with iterative refinement; DSCG and ICCG, diagonal scaling and incomplete Cholesky decomposition with conjugate gradient iteration (for symmetric positive definite matrices only); DSCGN and ILUGGN, diagonal scaling and incomplete LU decomposition with conjugate gradient interaction on the normal equations; DSBCG and ILUBCG, diagonal scaling and incomplete LU decomposition with bi-conjugate gradient iteration; and DSOMN and ILUOMN, diagonal scaling and incomplete LU decomposition with ORTHOMIN iteration

Linear program differentiation for single-channel speech separation

DEFF Research Database (Denmark)

Pearlmutter, Barak A.; Olsson, Rasmus Kongsgaard

2006-01-01

Many apparently difficult problems can be solved by reduction to linear programming. Such problems are often subproblems within larger systems. When gradient optimisation of the entire larger system is desired, it is necessary to propagate gradients through the internally-invoked LP solver....... For instance, when an intermediate quantity z is the solution to a linear program involving constraint matrix A, a vector of sensitivities dE/dz will induce sensitivities dE/dA. Here we show how these can be efficiently calculated, when they exist. This allows algorithmic differentiation to be applied...... to algorithms that invoke linear programming solvers as subroutines, as is common when using sparse representations in signal processing. Here we apply it to gradient optimisation of over complete dictionaries for maximally sparse representations of a speech corpus. The dictionaries are employed in a single...

An Improved Method for Solving Multiobjective Integer Linear Fractional Programming Problem

Directory of Open Access Journals (Sweden)

Meriem Ait Mehdi

2014-01-01

Full Text Available We describe an improvement of Chergui and Moulaï’s method (2008 that generates the whole efficient set of a multiobjective integer linear fractional program based on the branch and cut concept. The general step of this method consists in optimizing (maximizing without loss of generality one of the fractional objective functions over a subset of the original continuous feasible set; then if necessary, a branching process is carried out until obtaining an integer feasible solution. At this stage, an efficient cut is built from the criteria’s growth directions in order to discard a part of the feasible domain containing only nonefficient solutions. Our contribution concerns firstly the optimization process where a linear program that we define later will be solved at each step rather than a fractional linear program. Secondly, local ideal and nadir points will be used as bounds to prune some branches leading to nonefficient solutions. The computational experiments show that the new method outperforms the old one in all the treated instances.

Portfolio optimization by using linear programing models based on genetic algorithm

Science.gov (United States)

Sukono; Hidayat, Y.; Lesmana, E.; Putra, A. S.; Napitupulu, H.; Supian, S.

2018-01-01

In this paper, we discussed the investment portfolio optimization using linear programming model based on genetic algorithms. It is assumed that the portfolio risk is measured by absolute standard deviation, and each investor has a risk tolerance on the investment portfolio. To complete the investment portfolio optimization problem, the issue is arranged into a linear programming model. Furthermore, determination of the optimum solution for linear programming is done by using a genetic algorithm. As a numerical illustration, we analyze some of the stocks traded on the capital market in Indonesia. Based on the analysis, it is shown that the portfolio optimization performed by genetic algorithm approach produces more optimal efficient portfolio, compared to the portfolio optimization performed by a linear programming algorithm approach. Therefore, genetic algorithms can be considered as an alternative on determining the investment portfolio optimization, particularly using linear programming models.

Zhang neural network for online solution of time-varying convex quadratic program subject to time-varying linear-equality constraints

International Nuclear Information System (INIS)

Zhang Yunong; Li Zhan

2009-01-01

In this Letter, by following Zhang et al.'s method, a recurrent neural network (termed as Zhang neural network, ZNN) is developed and analyzed for solving online the time-varying convex quadratic-programming problem subject to time-varying linear-equality constraints. Different from conventional gradient-based neural networks (GNN), such a ZNN model makes full use of the time-derivative information of time-varying coefficient. The resultant ZNN model is theoretically proved to have global exponential convergence to the time-varying theoretical optimal solution of the investigated time-varying convex quadratic program. Computer-simulation results further substantiate the effectiveness, efficiency and novelty of such ZNN model and method.

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.

Planning under uncertainty solving large-scale stochastic linear programs

Energy Technology Data Exchange (ETDEWEB)

Infanger, G. [Stanford Univ., CA (United States). Dept. of Operations Research]|[Technische Univ., Vienna (Austria). Inst. fuer Energiewirtschaft

1992-12-01

For many practical problems, solutions obtained from deterministic models are unsatisfactory because they fail to hedge against certain contingencies that may occur in the future. Stochastic models address this shortcoming, but up to recently seemed to be intractable due to their size. Recent advances both in solution algorithms and in computer technology now allow us to solve important and general classes of practical stochastic problems. We show how large-scale stochastic linear programs can be efficiently solved by combining classical decomposition and Monte Carlo (importance) sampling techniques. We discuss the methodology for solving two-stage stochastic linear programs with recourse, present numerical results of large problems with numerous stochastic parameters, show how to efficiently implement the methodology on a parallel multi-computer and derive the theory for solving a general class of multi-stage problems with dependency of the stochastic parameters within a stage and between different stages.

A LINEAR PROGRAMMING ALGORITHM FOR LEAST-COST SCHEDULING

Directory of Open Access Journals (Sweden)

AYMAN H AL-MOMANI

1999-12-01

Full Text Available In this research, some concepts of linear programming and critical path method are reviewed to describe recent modeling structures that have been of great value in analyzing extended planning horizon project time-cost trade-offs problems. A simplified representation of a small project and a linear programming model is formulated to represent this system. Procedures to solve these various problems formulations were cited and the final solution is obtained using LINDO program. The model developed represents many restrictions and management considerations of the project. It could be used by construction managers in a planning stage to explore numerous possible opportunities to the contractor and predict the effect of a decision on the construction to facilitate a preferred operating policy given different management objectives. An implementation using this method is shown to outperform several other techniques and a large class of test problems. Linear programming show that the algorithm is very promising in practice on a wide variety of time-cost trade-offs problems. This method is simple, applicable to a large network, and generates a shorter computational time at low cost, along with an increase in robustness.

On the linear programming bound for linear Lee codes.

Science.gov (United States)

Astola, Helena; Tabus, Ioan

2016-01-01

Based on an invariance-type property of the Lee-compositions of a linear Lee code, additional equality constraints can be introduced to the linear programming problem of linear Lee codes. In this paper, we formulate this property in terms of an action of the multiplicative group of the field [Formula: see text] on the set of Lee-compositions. We show some useful properties of certain sums of Lee-numbers, which are the eigenvalues of the Lee association scheme, appearing in the linear programming problem of linear Lee codes. Using the additional equality constraints, we formulate the linear programming problem of linear Lee codes in a very compact form, leading to a fast execution, which allows to efficiently compute the bounds for large parameter values of the linear codes.

A Linear Programming Model to Optimize Various Objective Functions of a Foundation Type State Support Program.

Science.gov (United States)

Matzke, Orville R.

The purpose of this study was to formulate a linear programming model to simulate a foundation type support program and to apply this model to a state support program for the public elementary and secondary school districts in the State of Iowa. The model was successful in producing optimal solutions to five objective functions proposed for…

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...

Method for solving fully fuzzy linear programming problems using deviation degree measure

Institute of Scientific and Technical Information of China (English)

Haifang Cheng; Weilai Huang; Jianhu Cai

2013-01-01

A new ful y fuzzy linear programming (FFLP) prob-lem with fuzzy equality constraints is discussed. Using deviation degree measures, the FFLP problem is transformed into a crispδ-parametric linear programming (LP) problem. Giving the value of deviation degree in each constraint, the δ-fuzzy optimal so-lution of the FFLP problem can be obtained by solving this LP problem. An algorithm is also proposed to find a balance-fuzzy optimal solution between two goals in conflict: to improve the va-lues of the objective function and to decrease the values of the deviation degrees. A numerical example is solved to il ustrate the proposed method.

Economic planning for electric energy systems: a multi objective linearized approach for solution

International Nuclear Information System (INIS)

Mata Medeiros Branco, T. da.

1986-01-01

The economic planning problem associated to the expansion and operation of electrical power systems is considered in this study, represented for a vectorial objective function in which the minimization of resources involved and maximization of attended demand constitute goals to be satisfied. Supposing all the variables involved with linear characteristic and considering the conflict existing among the objectives to be achieved, in order to find a solution, a multi objective linearized approach is proposed. This approximation utilizes the compromise programming technique and linear programming methods. Generation and transmission are simultaneously considered into the optimization process in which associated losses and the capacity of each line are included. Illustrated examples are also presented with results discussed. (author)

Two-step algorithm of generalized PAPA method applied to linear programming solution of dynamic matrix control

International Nuclear Information System (INIS)

Shimizu, Yoshiaki

1991-01-01

In recent complicated nuclear systems, there are increasing demands for developing highly advanced procedures for various problems-solvings. Among them keen interests have been paid on man-machine communications to improve both safety and economy factors. Many optimization methods have been good enough to elaborate on these points. In this preliminary note, we will concern with application of linear programming (LP) for this purpose. First we will present a new superior version of the generalized PAPA method (GEPAPA) to solve LP problems. We will then examine its effectiveness when applied to derive dynamic matrix control (DMC) as the LP solution. The approach is to aim at the above goal through a quality control of process that will appear in the system. (author)

Communications oriented programming of parallel iterative solutions of sparse linear systems

Science.gov (United States)

Patrick, M. L.; Pratt, T. W.

1986-01-01

Parallel algorithms are developed for a class of scientific computational problems by partitioning the problems into smaller problems which may be solved concurrently. The effectiveness of the resulting parallel solutions is determined by the amount and frequency of communication and synchronization and the extent to which communication can be overlapped with computation. Three different parallel algorithms for solving the same class of problems are presented, and their effectiveness is analyzed from this point of view. The algorithms are programmed using a new programming environment. Run-time statistics and experience obtained from the execution of these programs assist in measuring the effectiveness of these algorithms.

CFORM- LINEAR CONTROL SYSTEM DESIGN AND ANALYSIS: CLOSED FORM SOLUTION AND TRANSIENT RESPONSE OF THE LINEAR DIFFERENTIAL EQUATION

Science.gov (United States)

Jamison, J. W.

1994-01-01

CFORM was developed by the Kennedy Space Center Robotics Lab to assist in linear control system design and analysis using closed form and transient response mechanisms. The program computes the closed form solution and transient response of a linear (constant coefficient) differential equation. CFORM allows a choice of three input functions: the Unit Step (a unit change in displacement); the Ramp function (step velocity); and the Parabolic function (step acceleration). It is only accurate in cases where the differential equation has distinct roots, and does not handle the case for roots at the origin (s=0). Initial conditions must be zero. Differential equations may be input to CFORM in two forms - polynomial and product of factors. In some linear control analyses, it may be more appropriate to use a related program, Linear Control System Design and Analysis (KSC-11376), which uses root locus and frequency response methods. CFORM was written in VAX FORTRAN for a VAX 11/780 under VAX VMS 4.7. It has a central memory requirement of 30K. CFORM was developed in 1987.

SLFP: a stochastic linear fractional programming approach for sustainable waste management.

Science.gov (United States)

Zhu, H; Huang, G H

2011-12-01

A stochastic linear fractional programming (SLFP) approach is developed for supporting sustainable municipal solid waste management under uncertainty. The SLFP method can solve ratio optimization problems associated with random information, where chance-constrained programming is integrated into a linear fractional programming framework. It has advantages in: (1) comparing objectives of two aspects, (2) reflecting system efficiency, (3) dealing with uncertainty expressed as probability distributions, and (4) providing optimal-ratio solutions under different system-reliability conditions. The method is applied to a case study of waste flow allocation within a municipal solid waste (MSW) management system. The obtained solutions are useful for identifying sustainable MSW management schemes with maximized system efficiency under various constraint-violation risks. The results indicate that SLFP can support in-depth analysis of the interrelationships among system efficiency, system cost and system-failure risk. Copyright © 2011 Elsevier Ltd. All rights reserved.

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.

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...

Linear-Algebra Programs

Science.gov (United States)

Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.

1982-01-01

The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.

Linear Programming Approaches for Power Savings in Software-defined Networks

NARCIS (Netherlands)

Moghaddam, F.A.; Grosso, P.

2016-01-01

Software-defined networks have been proposed as a viable solution to decrease the power consumption of the networking component in data center networks. Still the question remains on which scheduling algorithms are most suited to achieve this goal. We propose 4 different linear programming

A MICROCOMPUTER LINEAR PROGRAMMING PACKAGE: AN ALTERNATIVE TO MAINFRAMES

OpenAIRE

Laughlin, David H.

1984-01-01

This paper presents the capabilities and limitations of a microcomputer linear programming package. The solution algorithm is a version of the revised simplex. Rapid problem entry, user ease of operation, sensitivity analyses on objective function and right hand sides are advantages. A problem size of 150 activities and 64 constraints can be solved in present form. Due to problem size, limitations and lack of parametric and integer programming routines, this package is thought to have the mos...

Elementary linear programming with applications

CERN Document Server

Kolman, Bernard

1995-01-01

Linear programming finds the least expensive way to meet given needs with available resources. Its results are used in every area of engineering and commerce: agriculture, oil refining, banking, and air transport. Authors Kolman and Beck present the basic notions of linear programming and illustrate how they are used to solve important common problems. The software on the included disk leads students step-by-step through the calculations. The Second Edition is completely revised and provides additional review material on linear algebra as well as complete coverage of elementary linear program

adapta~k>n -11 of the surrogate memods for linear programming ...

African Journals Online (AJOL)

2005-08-02

Aug 2, 2005 ... inequality problem is made uj~ of the primal and dual optimal solutions for the given primal ... KEYWORDS: Linear Programming, Duality Theory, Surrogate Methods. ..... replaces x and the process IS repeated with the new x.

Comparison of linear, mixed integer and non-linear programming methods in energy system dispatch modelling

DEFF Research Database (Denmark)

Ommen, Torben Schmidt; Markussen, Wiebke Brix; Elmegaard, Brian

2014-01-01

In the paper, three frequently used operation optimisation methods are examined with respect to their impact on operation management of the combined utility technologies for electric power and DH (district heating) of eastern Denmark. The investigation focusses on individual plant operation...... differences and differences between the solution found by each optimisation method. One of the investigated approaches utilises LP (linear programming) for optimisation, one uses LP with binary operation constraints, while the third approach uses NLP (non-linear programming). The LP model is used...... as a benchmark, as this type is frequently used, and has the lowest amount of constraints of the three. A comparison of the optimised operation of a number of units shows significant differences between the three methods. Compared to the reference, the use of binary integer variables, increases operation...

Linear programming

CERN Document Server

Solow, Daniel

2014-01-01

This text covers the basic theory and computation for a first course in linear programming, including substantial material on mathematical proof techniques and sophisticated computation methods. Includes Appendix on using Excel. 1984 edition.

Stability of multi-objective bi-level linear programming problems under fuzziness

Directory of Open Access Journals (Sweden)

Abo-Sinna Mahmoud A.

2013-01-01

Full Text Available This paper deals with multi-objective bi-level linear programming problems under fuzzy environment. In the proposed method, tentative solutions are obtained and evaluated by using the partial information on preference of the decision-makers at each level. The existing results concerning the qualitative analysis of some basic notions in parametric linear programming problems are reformulated to study the stability of multi-objective bi-level linear programming problems. An algorithm for obtaining any subset of the parametric space, which has the same corresponding Pareto optimal solution, is presented. Also, this paper established the model for the supply-demand interaction in the age of electronic commerce (EC. First of all, the study uses the individual objectives of both parties as the foundation of the supply-demand interaction. Subsequently, it divides the interaction, in the age of electronic commerce, into the following two classifications: (i Market transactions, with the primary focus on the supply demand relationship in the marketplace; and (ii Information service, with the primary focus on the provider and the user of information service. By applying the bi-level programming technique of interaction process, the study will develop an analytical process to explain how supply-demand interaction achieves a compromise or why the process fails. Finally, a numerical example of information service is provided for the sake of illustration.

Rational approximations to solutions of linear differential equations.

Science.gov (United States)

Chudnovsky, D V; Chudnovsky, G V

1983-08-01

Rational approximations of Padé and Padé type to solutions of differential equations are considered. One of the main results is a theorem stating that a simultaneous approximation to arbitrary solutions of linear differential equations over C(x) cannot be "better" than trivial ones implied by the Dirichlet box principle. This constitutes, in particular, the solution in the linear case of Kolchin's problem that the "Roth's theorem" holds for arbitrary solutions of algebraic differential equations. Complete effective proofs for several valuations are presented based on the Wronskian methods and graded subrings of Picard-Vessiot extensions.

IESIP - AN IMPROVED EXPLORATORY SEARCH TECHNIQUE FOR PURE INTEGER LINEAR PROGRAMMING PROBLEMS

Science.gov (United States)

Fogle, F. R.

1994-01-01

IESIP, an Improved Exploratory Search Technique for Pure Integer Linear Programming Problems, addresses the problem of optimizing an objective function of one or more variables subject to a set of confining functions or constraints by a method called discrete optimization or integer programming. Integer programming is based on a specific form of the general linear programming problem in which all variables in the objective function and all variables in the constraints are integers. While more difficult, integer programming is required for accuracy when modeling systems with small numbers of components such as the distribution of goods, machine scheduling, and production scheduling. IESIP establishes a new methodology for solving pure integer programming problems by utilizing a modified version of the univariate exploratory move developed by Robert Hooke and T.A. Jeeves. IESIP also takes some of its technique from the greedy procedure and the idea of unit neighborhoods. A rounding scheme uses the continuous solution found by traditional methods (simplex or other suitable technique) and creates a feasible integer starting point. The Hook and Jeeves exploratory search is modified to accommodate integers and constraints and is then employed to determine an optimal integer solution from the feasible starting solution. The user-friendly IESIP allows for rapid solution of problems up to 10 variables in size (limited by DOS allocation). Sample problems compare IESIP solutions with the traditional branch-and-bound approach. IESIP is written in Borland's TURBO Pascal for IBM PC series computers and compatibles running DOS. Source code and an executable are provided. The main memory requirement for execution is 25K. This program is available on a 5.25 inch 360K MS DOS format diskette. IESIP was developed in 1990. IBM is a trademark of International Business Machines. TURBO Pascal is registered by Borland International.

A Study of Joint Cost Inclusion in Linear Programming Optimization

Directory of Open Access Journals (Sweden)

P. Armaos

2013-08-01

Full Text Available The concept of Structural Optimization has been a topic or research over the past century. Linear Programming Optimization has proved being the most reliable method of structural optimization. Global advances in linear programming optimization have been recently powered by University of Sheffield researchers, to include joint cost, self-weight and buckling considerations. A joint cost inclusion scopes to reduce the number of joints existing in an optimized structural solution, transforming it to a practically viable solution. The topic of the current paper is to investigate the effects of joint cost inclusion, as this is currently implemented in the optimization code. An extended literature review on this subject was conducted prior to familiarization with small scale optimization software. Using IntelliFORM software, a structured series of problems were set and analyzed. The joint cost tests examined benchmark problems and their consequent changes in the member topology, as the design domain was expanding. The findings of the analyses were remarkable and are being commented further on. The distinct topologies of solutions created by optimization processes are also recognized. Finally an alternative strategy of penalizing joints is presented.

Minimal solution of general dual fuzzy linear systems

International Nuclear Information System (INIS)

Abbasbandy, S.; Otadi, M.; Mosleh, M.

2008-01-01

Fuzzy linear systems of equations, play a major role in several applications in various area such as engineering, physics and economics. In this paper, we investigate the existence of a minimal solution of general dual fuzzy linear equation systems. Two necessary and sufficient conditions for the minimal solution existence are given. Also, some examples in engineering and economic are considered

Linear Programming and Network Flows

CERN Document Server

Bazaraa, Mokhtar S; Sherali, Hanif D

2011-01-01

The authoritative guide to modeling and solving complex problems with linear programming-extensively revised, expanded, and updated The only book to treat both linear programming techniques and network flows under one cover, Linear Programming and Network Flows, Fourth Edition has been completely updated with the latest developments on the topic. This new edition continues to successfully emphasize modeling concepts, the design and analysis of algorithms, and implementation strategies for problems in a variety of fields, including industrial engineering, management science, operations research

Waste management under multiple complexities: Inexact piecewise-linearization-based fuzzy flexible programming

International Nuclear Information System (INIS)

Sun Wei; Huang, Guo H.; Lv Ying; Li Gongchen

2012-01-01

Highlights: ► Inexact piecewise-linearization-based fuzzy flexible programming is proposed. ► It’s the first application to waste management under multiple complexities. ► It tackles nonlinear economies-of-scale effects in interval-parameter constraints. ► It estimates costs more accurately than the linear-regression-based model. ► Uncertainties are decreased and more satisfactory interval solutions are obtained. - Abstract: To tackle nonlinear economies-of-scale (EOS) effects in interval-parameter constraints for a representative waste management problem, an inexact piecewise-linearization-based fuzzy flexible programming (IPFP) model is developed. In IPFP, interval parameters for waste amounts and transportation/operation costs can be quantified; aspiration levels for net system costs, as well as tolerance intervals for both capacities of waste treatment facilities and waste generation rates can be reflected; and the nonlinear EOS effects transformed from objective function to constraints can be approximated. An interactive algorithm is proposed for solving the IPFP model, which in nature is an interval-parameter mixed-integer quadratically constrained programming model. To demonstrate the IPFP’s advantages, two alternative models are developed to compare their performances. One is a conventional linear-regression-based inexact fuzzy programming model (IPFP2) and the other is an IPFP model with all right-hand-sides of fussy constraints being the corresponding interval numbers (IPFP3). The comparison results between IPFP and IPFP2 indicate that the optimized waste amounts would have the similar patterns in both models. However, when dealing with EOS effects in constraints, the IPFP2 may underestimate the net system costs while the IPFP can estimate the costs more accurately. The comparison results between IPFP and IPFP3 indicate that their solutions would be significantly different. The decreased system uncertainties in IPFP’s solutions demonstrate

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.

Multiobjective fuzzy stochastic linear programming problems with inexact probability distribution

Energy Technology Data Exchange (ETDEWEB)

Hamadameen, Abdulqader Othman [Optimization, Department of Mathematical Sciences, Faculty of Science, UTM (Malaysia); Zainuddin, Zaitul Marlizawati [Department of Mathematical Sciences, Faculty of Science, UTM (Malaysia)

2014-06-19

This study deals with multiobjective fuzzy stochastic linear programming problems with uncertainty probability distribution which are defined as fuzzy assertions by ambiguous experts. The problem formulation has been presented and the two solutions strategies are; the fuzzy transformation via ranking function and the stochastic transformation when α{sup –}. cut technique and linguistic hedges are used in the uncertainty probability distribution. The development of Sen’s method is employed to find a compromise solution, supported by illustrative numerical example.

Optimal placement of capacitors in a radial network using conic and mixed integer linear programming

Energy Technology Data Exchange (ETDEWEB)

Jabr, R.A. [Electrical, Computer and Communication Engineering Department, Notre Dame University, P.O. Box: 72, Zouk Mikhael, Zouk Mosbeh (Lebanon)

2008-06-15

This paper considers the problem of optimally placing fixed and switched type capacitors in a radial distribution network. The aim of this problem is to minimize the costs associated with capacitor banks, peak power, and energy losses whilst satisfying a pre-specified set of physical and technical constraints. The proposed solution is obtained using a two-phase approach. In phase-I, the problem is formulated as a conic program in which all nodes are candidates for placement of capacitor banks whose sizes are considered as continuous variables. A global solution of the phase-I problem is obtained using an interior-point based conic programming solver. Phase-II seeks a practical optimal solution by considering capacitor sizes as discrete variables. The problem in this phase is formulated as a mixed integer linear program based on minimizing the L1-norm of deviations from the phase-I state variable values. The solution to the phase-II problem is obtained using a mixed integer linear programming solver. The proposed method is validated via extensive comparisons with previously published results. (author)

Analytical exact solution of the non-linear Schroedinger equation

International Nuclear Information System (INIS)

Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da

2011-01-01

Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)

General solutions of second-order linear difference equations of Euler type

Directory of Open Access Journals (Sweden)

Akane Hongyo

2017-01-01

Full Text Available The purpose of this paper is to give general solutions of linear difference equations which are related to the Euler-Cauchy differential equation \\(y^{\\prime\\prime}+(\\lambda/t^2y=0\\ or more general linear differential equations. We also show that the asymptotic behavior of solutions of the linear difference equations are similar to solutions of the linear differential equations.

A novel recurrent neural network with finite-time convergence for linear programming.

Science.gov (United States)

Liu, Qingshan; Cao, Jinde; Chen, Guanrong

2010-11-01

In this letter, a novel recurrent neural network based on the gradient method is proposed for solving linear programming problems. Finite-time convergence of the proposed neural network is proved by using the Lyapunov method. Compared with the existing neural networks for linear programming, the proposed neural network is globally convergent to exact optimal solutions in finite time, which is remarkable and rare in the literature of neural networks for optimization. Some numerical examples are given to show the effectiveness and excellent performance of the new recurrent neural network.

Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method

OpenAIRE

Aihong Ren

2016-01-01

This paper is concerned with a class of fully fuzzy bilevel linear programming problems where all the coefficients and decision variables of both objective functions and the constraints are fuzzy numbers. A new approach based on deviation degree measures and a ranking function method is proposed to solve these problems. We first introduce concepts of the feasible region and the fuzzy optimal solution of a fully fuzzy bilevel linear programming problem. In order to obtain a fuzzy optimal solut...

Comparison of open-source linear programming solvers.

Energy Technology Data Exchange (ETDEWEB)

Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin David.; Jones, Katherine A.; Martin, Nathaniel; Detry, Richard Joseph

2013-10-01

When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The solvers considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modular In-core Nonlinear Optimization System (MINOS) [6]. As no open-source solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.

Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method

Directory of Open Access Journals (Sweden)

Aihong Ren

2016-01-01

Full Text Available This paper is concerned with a class of fully fuzzy bilevel linear programming problems where all the coefficients and decision variables of both objective functions and the constraints are fuzzy numbers. A new approach based on deviation degree measures and a ranking function method is proposed to solve these problems. We first introduce concepts of the feasible region and the fuzzy optimal solution of a fully fuzzy bilevel linear programming problem. In order to obtain a fuzzy optimal solution of the problem, we apply deviation degree measures to deal with the fuzzy constraints and use a ranking function method of fuzzy numbers to rank the upper and lower level fuzzy objective functions. Then the fully fuzzy bilevel linear programming problem can be transformed into a deterministic bilevel programming problem. Considering the overall balance between improving objective function values and decreasing allowed deviation degrees, the computational procedure for finding a fuzzy optimal solution is proposed. Finally, a numerical example is provided to illustrate the proposed approach. The results indicate that the proposed approach gives a better optimal solution in comparison with the existing method.

Linear programming foundations and extensions

CERN Document Server

Vanderbei, Robert J

2001-01-01

Linear Programming: Foundations and Extensions is an introduction to the field of optimization. The book emphasizes constrained optimization, beginning with a substantial treatment of linear programming, and proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. The book is carefully written. Specific examples and concrete algorithms precede more abstract topics. Topics are clearly developed with a large number of numerical examples worked out in detail. Moreover, Linear Programming: Foundations and Extensions underscores the purpose of optimization: to solve practical problems on a computer. Accordingly, the book is coordinated with free efficient C programs that implement the major algorithms studied: -The two-phase simplex method; -The primal-dual simplex method; -The path-following interior-point method; -The homogeneous self-dual methods. In addition, there are online JAVA applets that illustrate various pivot rules and variants of the simplex m...

TOEPLITZ, Solution of Linear Equation System with Toeplitz or Circulant Matrix

International Nuclear Information System (INIS)

Garbow, B.

1984-01-01

Description of program or function: TOEPLITZ is a collection of FORTRAN subroutines for solving linear systems Ax=b, where A is a Toeplitz matrix, a Circulant matrix, or has one or several block structures based on Toeplitz or Circulant matrices. Such systems arise in problems of electrodynamics, acoustics, mathematical statistics, algebra, in the numerical solution of integral equations with a difference kernel, and in the theory of stationary time series and signals

Ada Linear-Algebra Program

Science.gov (United States)

Klumpp, A. R.; Lawson, C. L.

1988-01-01

Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.

The application of the fall-vector method in decomposition schemes for the solution of integer linear programming problems

International Nuclear Information System (INIS)

Sergienko, I.V.; Golodnikov, A.N.

1984-01-01

This article applies the methods of decompositions, which are used to solve continuous linear problems, to integer and partially integer problems. The fall-vector method is used to solve the obtained coordinate problems. An algorithm of the fall-vector is described. The Kornai-Liptak decomposition principle is used to reduce the integer linear programming problem to integer linear programming problems of a smaller dimension and to a discrete coordinate problem with simple constraints

Solution of linear ill-posed problems using overcomplete dictionaries

OpenAIRE

Pensky, Marianna

2016-01-01

In the present paper we consider application of overcomplete dictionaries to solution of general ill-posed linear inverse problems. Construction of an adaptive optimal solution for such problems usually relies either on a singular value decomposition or representation of the solution via an orthonormal basis. The shortcoming of both approaches lies in the fact that, in many situations, neither the eigenbasis of the linear operator nor a standard orthonormal basis constitutes an appropriate co...

Fuzzy linear programming based optimal fuel scheduling incorporating blending/transloading facilities

Energy Technology Data Exchange (ETDEWEB)

Djukanovic, M.; Babic, B.; Milosevic, B. [Electrical Engineering Inst. Nikola Tesla, Belgrade (Yugoslavia); Sobajic, D.J. [EPRI, Palo Alto, CA (United States). Power System Control; Pao, Y.H. [Case Western Reserve Univ., Cleveland, OH (United States)]|[AI WARE, Inc., Cleveland, OH (United States)

1996-05-01

In this paper the blending/transloading facilities are modeled using an interactive fuzzy linear programming (FLP), in order to allow the decision-maker to solve the problem of uncertainty of input information within the fuel scheduling optimization. An interactive decision-making process is formulated in which decision-maker can learn to recognize good solutions by considering all possibilities of fuzziness. The application of the fuzzy formulation is accompanied by a careful examination of the definition of fuzziness, appropriateness of the membership function and interpretation of results. The proposed concept provides a decision support system with integration-oriented features, whereby the decision-maker can learn to recognize the relative importance of factors in the specific domain of optimal fuel scheduling (OFS) problem. The formulation of a fuzzy linear programming problem to obtain a reasonable nonfuzzy solution under consideration of the ambiguity of parameters, represented by fuzzy numbers, is introduced. An additional advantage of the FLP formulation is its ability to deal with multi-objective problems.

Linear genetic programming

CERN Document Server

Brameier, Markus

2007-01-01

Presents a variant of Genetic Programming that evolves imperative computer programs as linear sequences of instructions, in contrast to the more traditional functional expressions or syntax trees. This book serves as a reference for researchers, but also contains sufficient introduction for students and those who are new to the field

The linear programming bound for binary linear codes

NARCIS (Netherlands)

Brouwer, A.E.

1993-01-01

Combining Delsarte's (1973) linear programming bound with the information that certain weights cannot occur, new upper bounds for dmin (n,k), the maximum possible minimum distance of a binary linear code with given word length n and dimension k, are derived.

Linear Programming across the Curriculum

Science.gov (United States)

Yoder, S. Elizabeth; Kurz, M. Elizabeth

2015-01-01

Linear programming (LP) is taught in different departments across college campuses with engineering and management curricula. Modeling an LP problem is taught in every linear programming class. As faculty teaching in Engineering and Management departments, the depth to which teachers should expect students to master this particular type of…

Linear programming

CERN Document Server

Karloff, Howard

1991-01-01

To this reviewer’s knowledge, this is the first book accessible to the upper division undergraduate or beginning graduate student that surveys linear programming from the Simplex Method…via the Ellipsoid algorithm to Karmarkar’s algorithm. Moreover, its point of view is algorithmic and thus it provides both a history and a case history of work in complexity theory. The presentation is admirable; Karloff's style is informal (even humorous at times) without sacrificing anything necessary for understanding. Diagrams (including horizontal brackets that group terms) aid in providing clarity. The end-of-chapter notes are helpful...Recommended highly for acquisition, since it is not only a textbook, but can also be used for independent reading and study. —Choice Reviews The reader will be well served by reading the monograph from cover to cover. The author succeeds in providing a concise, readable, understandable introduction to modern linear programming. —Mathematics of Computing This is a textbook intend...

Mass Optimization of Battery/Supercapacitors Hybrid Systems Based on a Linear Programming Approach

Science.gov (United States)

Fleury, Benoit; Labbe, Julien

2014-08-01

The objective of this paper is to show that, on a specific launcher-type mission profile, a 40% gain of mass is expected using a battery/supercapacitors active hybridization instead of a single battery solution. This result is based on the use of a linear programming optimization approach to perform the mass optimization of the hybrid power supply solution.

Reduced-Size Integer Linear Programming Models for String Selection Problems: Application to the Farthest String Problem.

Science.gov (United States)

Zörnig, Peter

2015-08-01

We present integer programming models for some variants of the farthest string problem. The number of variables and constraints is substantially less than that of the integer linear programming models known in the literature. Moreover, the solution of the linear programming-relaxation contains only a small proportion of noninteger values, which considerably simplifies the rounding process. Numerical tests have shown excellent results, especially when a small set of long sequences is given.

Topics in computational linear optimization

DEFF Research Database (Denmark)

Hultberg, Tim Helge

2000-01-01

Linear optimization has been an active area of research ever since the pioneering work of G. Dantzig more than 50 years ago. This research has produced a long sequence of practical as well as theoretical improvements of the solution techniques avilable for solving linear optimization problems...... of high quality solvers and the use of algebraic modelling systems to handle the communication between the modeller and the solver. This dissertation features four topics in computational linear optimization: A) automatic reformulation of mixed 0/1 linear programs, B) direct solution of sparse unsymmetric...... systems of linear equations, C) reduction of linear programs and D) integration of algebraic modelling of linear optimization problems in C++. Each of these topics is treated in a separate paper included in this dissertation. The efficiency of solving mixed 0-1 linear programs by linear programming based...

Investigating Integer Restrictions in Linear Programming

Science.gov (United States)

Edwards, Thomas G.; Chelst, Kenneth R.; Principato, Angela M.; Wilhelm, Thad L.

2015-01-01

Linear programming (LP) is an application of graphing linear systems that appears in many Algebra 2 textbooks. Although not explicitly mentioned in the Common Core State Standards for Mathematics, linear programming blends seamlessly into modeling with mathematics, the fourth Standard for Mathematical Practice (CCSSI 2010, p. 7). In solving a…

Visual, Algebraic and Mixed Strategies in Visually Presented Linear Programming Problems.

Science.gov (United States)

Shama, Gilli; Dreyfus, Tommy

1994-01-01

Identified and classified solution strategies of (n=49) 10th-grade students who were presented with linear programming problems in a predominantly visual setting in the form of a computerized game. Visual strategies were developed more frequently than either algebraic or mixed strategies. Appendix includes questionnaires. (Contains 11 references.)…

Large-time asymptotic behaviour of solutions of non-linear Sobolev-type equations

International Nuclear Information System (INIS)

Kaikina, Elena I; Naumkin, Pavel I; Shishmarev, Il'ya A

2009-01-01

The large-time asymptotic behaviour of solutions of the Cauchy problem is investigated for a non-linear Sobolev-type equation with dissipation. For small initial data the approach taken is based on a detailed analysis of the Green's function of the linear problem and the use of the contraction mapping method. The case of large initial data is also closely considered. In the supercritical case the asymptotic formulae are quasi-linear. The asymptotic behaviour of solutions of a non-linear Sobolev-type equation with a critical non-linearity of the non-convective kind differs by a logarithmic correction term from the behaviour of solutions of the corresponding linear equation. For a critical convective non-linearity, as well as for a subcritical non-convective non-linearity it is proved that the leading term of the asymptotic expression for large times is a self-similar solution. For Sobolev equations with convective non-linearity the asymptotic behaviour of solutions in the subcritical case is the product of a rarefaction wave and a shock wave. Bibliography: 84 titles.

Minimization of Linear Functionals Defined on| Solutions of Large-Scale Discrete Ill-Posed Problems

DEFF Research Database (Denmark)

Elden, Lars; Hansen, Per Christian; Rojas, Marielba

2003-01-01

The minimization of linear functionals de ned on the solutions of discrete ill-posed problems arises, e.g., in the computation of con dence intervals for these solutions. In 1990, Elden proposed an algorithm for this minimization problem based on a parametric-programming reformulation involving...... the solution of a sequence of trust-region problems, and using matrix factorizations. In this paper, we describe MLFIP, a large-scale version of this algorithm where a limited-memory trust-region solver is used on the subproblems. We illustrate the use of our algorithm in connection with an inverse heat...

General solution of linear vector supersymmetry

International Nuclear Information System (INIS)

Blasi, Alberto; Maggiore, Nicola

2007-01-01

We give the general solution of the Ward identity for the linear vector supersymmetry which characterizes all topological models. Such a solution, whose expression is quite compact and simple, greatly simplifies the study of theories displaying a supersymmetric algebraic structure, reducing to a few lines the proof of their possible finiteness. In particular, the cohomology technology, usually involved for the quantum extension of these theories, is completely bypassed. The case of Chern-Simons theory is taken as an example

APPLYING ROBUST RANKING METHOD IN TWO PHASE FUZZY OPTIMIZATION LINEAR PROGRAMMING PROBLEMS (FOLPP

Directory of Open Access Journals (Sweden)

Monalisha Pattnaik

2014-12-01

Full Text Available Background: This paper explores the solutions to the fuzzy optimization linear program problems (FOLPP where some parameters are fuzzy numbers. In practice, there are many problems in which all decision parameters are fuzzy numbers, and such problems are usually solved by either probabilistic programming or multi-objective programming methods. Methods: In this paper, using the concept of comparison of fuzzy numbers, a very effective method is introduced for solving these problems. This paper extends linear programming based problem in fuzzy environment. With the problem assumptions, the optimal solution can still be theoretically solved using the two phase simplex based method in fuzzy environment. To handle the fuzzy decision variables can be initially generated and then solved and improved sequentially using the fuzzy decision approach by introducing robust ranking technique. Results and conclusions: The model is illustrated with an application and a post optimal analysis approach is obtained. The proposed procedure was programmed with MATLAB (R2009a version software for plotting the four dimensional slice diagram to the application. Finally, numerical example is presented to illustrate the effectiveness of the theoretical results, and to gain additional managerial insights. 

Numerical solution of large sparse linear systems

International Nuclear Information System (INIS)

Meurant, Gerard; Golub, Gene.

1982-02-01

This note is based on one of the lectures given at the 1980 CEA-EDF-INRIA Numerical Analysis Summer School whose aim is the study of large sparse linear systems. The main topics are solving least squares problems by orthogonal transformation, fast Poisson solvers and solution of sparse linear system by iterative methods with a special emphasis on preconditioned conjuguate gradient method [fr

Solutions to estimation problems for scalar hamilton-jacobi equations using linear programming

KAUST Repository

Claudel, Christian G.; Chamoin, Timothee; Bayen, Alexandre M.

2014-01-01

This brief presents new convex formulations for solving estimation problems in systems modeled by scalar Hamilton-Jacobi (HJ) equations. Using a semi-analytic formula, we show that the constraints resulting from a HJ equation are convex, and can be written as a set of linear inequalities. We use this fact to pose various (and seemingly unrelated) estimation problems related to traffic flow-engineering as a set of linear programs. In particular, we solve data assimilation and data reconciliation problems for estimating the state of a system when the model and measurement constraints are incompatible. We also solve traffic estimation problems, such as travel time estimation or density estimation. For all these problems, a numerical implementation is performed using experimental data from the Mobile Century experiment. In the context of reproducible research, the code and data used to compute the results presented in this brief have been posted online and are accessible to regenerate the results. © 2013 IEEE.

PCX, Interior-Point Linear Programming Solver

International Nuclear Information System (INIS)

Czyzyk, J.

2004-01-01

1 - Description of program or function: PCX solves linear programming problems using the Mehrota predictor-corrector interior-point algorithm. PCX can be called as a subroutine or used in stand-alone mode, with data supplied from an MPS file. The software incorporates modules that can be used separately from the linear programming solver, including a pre-solve routine and data structure definitions. 2 - Methods: The Mehrota predictor-corrector method is a primal-dual interior-point method for linear programming. The starting point is determined from a modified least squares heuristic. Linear systems of equations are solved at each interior-point iteration via a sparse Cholesky algorithm native to the code. A pre-solver is incorporated in the code to eliminate inefficiencies in the user's formulation of the problem. 3 - Restriction on the complexity of the problem: There are no size limitations built into the program. The size of problem solved is limited by RAM and swap space on the user's computer

Sensitivity Analysis of Linear Programming and Quadratic Programming Algorithms for Control Allocation

Science.gov (United States)

Frost, Susan A.; Bodson, Marc; Acosta, Diana M.

2009-01-01

The Next Generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five effectors, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude and flight path of the aircraft. The NextGen aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship does not exist anymore between the required effector deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands and attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples that the solutions provided using the l2 norm of quadratic programming are less sensitive than those using the l1 norm of linear programming.

Riccati transformations and principal solutions of discrete linear systems

International Nuclear Information System (INIS)

Ahlbrandt, C.D.; Hooker, J.W.

1984-01-01

Consider a second-order linear matrix difference equation. A definition of principal and anti-principal, or recessive and dominant, solutions of the equation are given and the existence of principal and anti-principal solutions and the essential uniqueness of principal solutions is proven

Solution of the fully fuzzy linear systems using iterative techniques

International Nuclear Information System (INIS)

Dehghan, Mehdi; Hashemi, Behnam; Ghatee, Mehdi

2007-01-01

This paper mainly intends to discuss the iterative solution of fully fuzzy linear systems which we call FFLS. We employ Dubois and Prade's approximate arithmetic operators on LR fuzzy numbers for finding a positive fuzzy vector x-tilde which satisfies A-tildex-tilde=b, where A-tilde and b-tilde are a fuzzy matrix and a fuzzy vector, respectively. Please note that the positivity assumption is not so restrictive in applied problems. We transform FFLS and propose iterative techniques such as Richardson, Jacobi, Jacobi overrelaxation (JOR), Gauss-Seidel, successive overrelaxation (SOR), accelerated overrelaxation (AOR), symmetric and unsymmetric SOR (SSOR and USSOR) and extrapolated modified Aitken (EMA) for solving FFLS. In addition, the methods of Newton, quasi-Newton and conjugate gradient are proposed from nonlinear programming for solving a fully fuzzy linear system. Various numerical examples are also given to show the efficiency of the proposed schemes

Numerical solution of two-dimensional non-linear partial differential ...

African Journals Online (AJOL)

linear partial differential equations using a hybrid method. The solution technique involves discritizing the non-linear system of partial differential equations (PDEs) to obtain a corresponding nonlinear system of algebraic difference equations to be ...

A primal-dual exterior point algorithm for linear programming problems

Directory of Open Access Journals (Sweden)

Samaras Nikolaos

2009-01-01

Full Text Available The aim of this paper is to present a new simplex type algorithm for the Linear Programming Problem. The Primal - Dual method is a Simplex - type pivoting algorithm that generates two paths in order to converge to the optimal solution. The first path is primal feasible while the second one is dual feasible for the original problem. Specifically, we use a three-phase-implementation. The first two phases construct the required primal and dual feasible solutions, using the Primal Simplex algorithm. Finally, in the third phase the Primal - Dual algorithm is applied. Moreover, a computational study has been carried out, using randomly generated sparse optimal linear problems, to compare its computational efficiency with the Primal Simplex algorithm and also with MATLAB's Interior Point Method implementation. The algorithm appears to be very promising since it clearly shows its superiority to the Primal Simplex algorithm as well as its robustness over the IPM algorithm.

Ranking Forestry Investments With Parametric Linear Programming

Science.gov (United States)

Paul A. Murphy

1976-01-01

Parametric linear programming is introduced as a technique for ranking forestry investments under multiple constraints; it combines the advantages of simple tanking and linear programming as capital budgeting tools.

Oscillatory behaviour of solutions of linear neutral differential ...

African Journals Online (AJOL)

The paper considers the contribution of space-time noise to the oscillatory behaviour of solutions of a linear neutral stochastic delay differential equation. It was established that under certain conditions on the time lags and their speed of adjustments, the presence of noise generates oscillation in the solution of the equation ...

A penalization approach to linear programming duality with application to capacity constrained transport

OpenAIRE

Korman, Jonathan; McCann, Robert J.; Seis, Christian

2013-01-01

A new approach to linear programming duality is proposed which relies on quadratic penalization, so that the relation between solutions to the penalized primal and dual problems becomes affine. This yields a new proof of Levin's duality theorem for capacity-constrained optimal transport as an infinite-dimensional application.

Introduction to linear programming: Coalitional game experiments

Energy Technology Data Exchange (ETDEWEB)

Lucas, W.

1994-12-31

Many solution notions in the multiperson cooperative games (in characteristic function form) make use of linear programming (LP). The popular concept of the {open_quotes}core{close_quotes} of a coalitional game is a special type of LP. It can be introduced in a very simple and quite exciting manner by means of a group experiment. A total of fifty dollars will be given to three randomly selected attendees who will take part in an experiment during this talk, presuming they behave in a Pareto optimal manner. Furthermore, the dual of the particular LP for the core gives rise to the idea of {open_quotes}balanced sets{close_quotes} which is an interesting combinatorial structure in its own right.

Novel methods for Solving Economic Dispatch of Security-Constrained Unit Commitment Based on Linear Programming

Science.gov (United States)

Guo, Sangang

2017-09-01

There are two stages in solving security-constrained unit commitment problems (SCUC) within Lagrangian framework: one is to obtain feasible units’ states (UC), the other is power economic dispatch (ED) for each unit. The accurate solution of ED is more important for enhancing the efficiency of the solution to SCUC for the fixed feasible units’ statues. Two novel methods named after Convex Combinatorial Coefficient Method and Power Increment Method respectively based on linear programming problem for solving ED are proposed by the piecewise linear approximation to the nonlinear convex fuel cost functions. Numerical testing results show that the methods are effective and efficient.

Linear programming algorithms and applications

CERN Document Server

Vajda, S

1981-01-01

This text is based on a course of about 16 hours lectures to students of mathematics, statistics, and/or operational research. It is intended to introduce readers to the very wide range of applicability of linear programming, covering problems of manage­ ment, administration, transportation and a number of other uses which are mentioned in their context. The emphasis is on numerical algorithms, which are illustrated by examples of such modest size that the solutions can be obtained using pen and paper. It is clear that these methods, if applied to larger problems, can also be carried out on automatic (electronic) computers. Commercially available computer packages are, in fact, mainly based on algorithms explained in this book. The author is convinced that the user of these algorithms ought to be knowledgeable about the underlying theory. Therefore this volume is not merely addressed to the practitioner, but also to the mathematician who is interested in relatively new developments in algebraic theory and in...

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

Linear perturbations of a self-similar solution of hydrodynamics with non-linear heat conduction

International Nuclear Information System (INIS)

Dubois-Boudesocque, Carine

2000-01-01

The stability of an ablative flow, where a shock wave is located upstream a thermal front, is of importance in inertial confinement fusion. The present model considers an exact self-similar solution to the hydrodynamic equations with non-linear heat conduction for a semi-infinite slab. For lack of an analytical solution, a high resolution numerical procedure is devised, which couples a finite difference method with a relaxation algorithm using a two-domain pseudo-spectral method. Stability of this solution is studied by introducing linear perturbation method within a Lagrangian-Eulerian framework. The initial and boundary value problem is solved by a splitting of the equations between a hyperbolic system and a parabolic equation. The boundary conditions of the hyperbolic system are treated, in the case of spectral methods, according to Thompson's approach. The parabolic equation is solved by an influence matrix method. These numerical procedures have been tested versus exact solutions. Considering a boundary heat flux perturbation, the space-time evolution of density, velocity and temperature are shown. (author) [fr

Oscillatory solutions of the Cauchy problem for linear differential equations

Directory of Open Access Journals (Sweden)

Gro Hovhannisyan

2015-06-01

Full Text Available We consider the Cauchy problem for second and third order linear differential equations with constant complex coefficients. We describe necessary and sufficient conditions on the data for the existence of oscillatory solutions. It is known that in the case of real coefficients the oscillatory behavior of solutions does not depend on initial values, but we show that this is no longer true in the complex case: hence in practice it is possible to control oscillatory behavior by varying the initial conditions. Our Proofs are based on asymptotic analysis of the zeros of solutions, represented as linear combinations of exponential functions.

A Linear Programming Approach to Routing Control in Networks of Constrained Nonlinear Positive Systems with Concave Flow Rates

Science.gov (United States)

Arneson, Heather M.; Dousse, Nicholas; Langbort, Cedric

2014-01-01

We consider control design for positive compartmental systems in which each compartment's outflow rate is described by a concave function of the amount of material in the compartment.We address the problem of determining the routing of material between compartments to satisfy time-varying state constraints while ensuring that material reaches its intended destination over a finite time horizon. We give sufficient conditions for the existence of a time-varying state-dependent routing strategy which ensures that the closed-loop system satisfies basic network properties of positivity, conservation and interconnection while ensuring that capacity constraints are satisfied, when possible, or adjusted if a solution cannot be found. These conditions are formulated as a linear programming problem. Instances of this linear programming problem can be solved iteratively to generate a solution to the finite horizon routing problem. Results are given for the application of this control design method to an example problem. Key words: linear programming; control of networks; positive systems; controller constraints and structure.

An Interactive Method to Solve Infeasibility in Linear Programming Test Assembling Models

Science.gov (United States)

Huitzing, Hiddo A.

2004-01-01

In optimal assembly of tests from item banks, linear programming (LP) models have proved to be very useful. Assembly by hand has become nearly impossible, but these LP techniques are able to find the best solutions, given the demands and needs of the test to be assembled and the specifics of the item bank from which it is assembled. However,…

Robust Control Design via Linear Programming

Science.gov (United States)

Keel, L. H.; Bhattacharyya, S. P.

1998-01-01

This paper deals with the problem of synthesizing or designing a feedback controller of fixed dynamic order. The closed loop specifications considered here are given in terms of a target performance vector representing a desired set of closed loop transfer functions connecting various signals. In general these point targets are unattainable with a fixed order controller. By enlarging the target from a fixed point set to an interval set the solvability conditions with a fixed order controller are relaxed and a solution is more easily enabled. Results from the parametric robust control literature can be used to design the interval target family so that the performance deterioration is acceptable, even when plant uncertainty is present. It is shown that it is possible to devise a computationally simple linear programming approach that attempts to meet the desired closed loop specifications.

Interior Point Method for Solving Fuzzy Number Linear Programming Problems Using Linear Ranking Function

Directory of Open Access Journals (Sweden)

Yi-hua Zhong

2013-01-01

Full Text Available Recently, various methods have been developed for solving linear programming problems with fuzzy number, such as simplex method and dual simplex method. But their computational complexities are exponential, which is not satisfactory for solving large-scale fuzzy linear programming problems, especially in the engineering field. A new method which can solve large-scale fuzzy number linear programming problems is presented in this paper, which is named a revised interior point method. Its idea is similar to that of interior point method used for solving linear programming problems in crisp environment before, but its feasible direction and step size are chosen by using trapezoidal fuzzy numbers, linear ranking function, fuzzy vector, and their operations, and its end condition is involved in linear ranking function. Their correctness and rationality are proved. Moreover, choice of the initial interior point and some factors influencing the results of this method are also discussed and analyzed. The result of algorithm analysis and example study that shows proper safety factor parameter, accuracy parameter, and initial interior point of this method may reduce iterations and they can be selected easily according to the actual needs. Finally, the method proposed in this paper is an alternative method for solving fuzzy number linear programming problems.

Constructive Development of the Solutions of Linear Equations in Introductory Ordinary Differential Equations

Science.gov (United States)

Mallet, D. G.; McCue, S. W.

2009-01-01

The solution of linear ordinary differential equations (ODEs) is commonly taught in first-year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognizing what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to…

Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control

Energy Technology Data Exchange (ETDEWEB)

Gaitsgory, Vladimir, E-mail: vladimir.gaitsgory@mq.edu.au [Macquarie University, Department of Mathematics (Australia); Rossomakhine, Sergey, E-mail: serguei.rossomakhine@flinders.edu.au [Flinders University, Flinders Mathematical Sciences Laboratory, School of Computer Science, Engineering and Mathematics (Australia)

2015-04-15

The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.

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,…

Sparsity Prevention Pivoting Method for Linear Programming

DEFF Research Database (Denmark)

Li, Peiqiang; Li, Qiyuan; Li, Canbing

2018-01-01

When the simplex algorithm is used to calculate a linear programming problem, if the matrix is a sparse matrix, it will be possible to lead to many zero-length calculation steps, and even iterative cycle will appear. To deal with the problem, a new pivoting method is proposed in this paper....... The principle of this method is avoided choosing the row which the value of the element in the b vector is zero as the row of the pivot element to make the matrix in linear programming density and ensure that most subsequent steps will improve the value of the objective function. One step following...... this principle is inserted to reselect the pivot element in the existing linear programming algorithm. Both the conditions for inserting this step and the maximum number of allowed insertion steps are determined. In the case study, taking several numbers of linear programming problems as examples, the results...

Sparsity Prevention Pivoting Method for Linear Programming

DEFF Research Database (Denmark)

Li, Peiqiang; Li, Qiyuan; Li, Canbing

2018-01-01

. The principle of this method is avoided choosing the row which the value of the element in the b vector is zero as the row of the pivot element to make the matrix in linear programming density and ensure that most subsequent steps will improve the value of the objective function. One step following......When the simplex algorithm is used to calculate a linear programming problem, if the matrix is a sparse matrix, it will be possible to lead to many zero-length calculation steps, and even iterative cycle will appear. To deal with the problem, a new pivoting method is proposed in this paper...... this principle is inserted to reselect the pivot element in the existing linear programming algorithm. Both the conditions for inserting this step and the maximum number of allowed insertion steps are determined. In the case study, taking several numbers of linear programming problems as examples, the results...

Linear programming model for solution of matrix game with payoffs trapezoidal intuitionistic fuzzy number

Directory of Open Access Journals (Sweden)

Darunee Hunwisai

2017-01-01

Full Text Available In this work, we considered two-person zero-sum games with fuzzy payoffs and matrix games with payoffs of trapezoidal intuitionistic fuzzy numbers (TrIFNs. The concepts of TrIFNs and their arithmetic operations were used. The cut-set based method for matrix game with payoffs of TrIFNs was also considered. Compute the interval-type value of any alfa-constrategies by simplex method for linear programming. The proposed method is illustrated with a numerical example.

Exponential estimates for solutions of half-linear differential equations

Czech Academy of Sciences Publication Activity Database

Řehák, Pavel

2015-01-01

Roč. 147, č. 1 (2015), s. 158-171 ISSN 0236-5294 Institutional support: RVO:67985840 Keywords : half-linear differential equation * decreasing solution * increasing solution * asymptotic behavior Subject RIV: BA - General Mathematics Impact factor: 0.469, year: 2015 http://link.springer.com/article/10.1007%2Fs10474-015-0522-9

Linear programming models and methods of matrix games with payoffs of triangular fuzzy numbers

CERN Document Server

Li, Deng-Feng

2016-01-01

This book addresses two-person zero-sum finite games in which the payoffs in any situation are expressed with fuzzy numbers. The purpose of this book is to develop a suite of effective and efficient linear programming models and methods for solving matrix games with payoffs in fuzzy numbers. Divided into six chapters, it discusses the concepts of solutions of matrix games with payoffs of intervals, along with their linear programming models and methods. Furthermore, it is directly relevant to the research field of matrix games under uncertain economic management. The book offers a valuable resource for readers involved in theoretical research and practical applications from a range of different fields including game theory, operational research, management science, fuzzy mathematical programming, fuzzy mathematics, industrial engineering, business and social economics. .

A solution approach for non-linear analysis of concrete members

International Nuclear Information System (INIS)

Hadi, N. M.; Das, S.

1999-01-01

Non-linear solution of reinforced concrete structural members, at and beyond its maximum strength poses complex numerical problems. This is due to the fact that concrete exhibits strain softening behaviour once it reaches its maximum strength. This paper introduces an improved non-linear solution capable to overcome the numerical problems efficiently. The paper also presents a new concept of modeling discrete cracks in concrete members by using gap elements. Gap elements are placed in between two adjacent concrete elements in tensile zone. The magnitude of elongation of gap elements, which represents the width of the crack in concrete, increases edith the increase of tensile stress in those elements. As a result, transfer of local from one concrete element to adjacent elements reduces. Results of non-linear finite element analysis of three concrete beams using this new solution strategy are compared with those obtained by other researchers, and a good agreement is achieved. (authors). 13 refs. 9 figs.,

Dose optimization based on linear programming implemented in a system for treatment planning in Monte Carlo

International Nuclear Information System (INIS)

Ureba, A.; Palma, B. A.; Leal, A.

2011-01-01

Develop a more efficient method of optimization in relation to time, based on linear programming designed to implement a multi objective penalty function which also permits a simultaneous solution integrated boost situations considering two white volumes simultaneously.

Timetabling an Academic Department with Linear Programming.

Science.gov (United States)

Bezeau, Lawrence M.

This paper describes an approach to faculty timetabling and course scheduling that uses computerized linear programming. After reviewing the literature on linear programming, the paper discusses the process whereby a timetable was created for a department at the University of New Brunswick. Faculty were surveyed with respect to course offerings…

Subroutine for series solutions of linear differential equations

International Nuclear Information System (INIS)

Tasso, H.; Steuerwald, J.

1976-02-01

A subroutine for Taylor series solutions of systems of ordinary linear differential equations is descriebed. It uses the old idea of Lie series but allows simple implementation and is time-saving for symbolic manipulations. (orig.) [de

Numerical Methods for Solution of the Extended Linear Quadratic Control Problem

DEFF Research Database (Denmark)

Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog

2012-01-01

In this paper we present the extended linear quadratic control problem, its efficient solution, and a discussion of how it arises in the numerical solution of nonlinear model predictive control problems. The extended linear quadratic control problem is the optimal control problem corresponding...... to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...... and discuss instances in which it arises. The methods discussed in the paper have been implemented in efficient C code for both CPUs and GPUs for a number of test examples....

Optimization of production planning in Czech agricultural co-operative via linear programming

Directory of Open Access Journals (Sweden)

Jitka Janová

2009-01-01

Full Text Available The production planning is one of the key managerial decisions in agricultural business, which must be done periodically every year. Correct decision must cover the agriculture demands of planting the crops such as crop rotation restrictions or water resource scarcity, while the decision maker aims to plan the crop design in most profitable way in sense of maximizing the total profit from the crop yield. This decision problem represents the optimization of crop design and can be treated by the me­thods of linear programming which begun to be extensively used in agriculture production planning in USA during 50’s. There is ongoing research of mathematical programming applications in agriculture worldwide, but the results are not easily transferable to other localities due to the specific local restrictions in each country. In Czech Republic the farmers use for production planning mainly their expert knowledge and past experience. However, the mathematical programming approach enables find the true optimal solution of the problem, which especially in the problems with a great number of constraints is not easy to find intuitively. One of the possible barriers for using the general decision support systems (which are based on mathematical programming methods for agriculture production planning in Czech Republic is its expensiveness. The small farmer can not afford to buy the expensive software or to employ a mathematical programming specialist. The aim of this paper is to present a user friendly linear programming model of the typical agricultural production planning problem in Czech Republic which can be solved via software tools commonly available in any farm (e.g. EXCEL. The linear programming model covering the restrictions on total costs, crop rotation, thresholds for the total area sowed by particular crops, total amount of manure and the need of feed crops is developed. The model is applied in real-world problem of Czech agriculture

The linear ordering problem: an algorithm for the optimal solution ...

African Journals Online (AJOL)

In this paper we describe and implement an algorithm for the exact solution of the Linear Ordering problem. Linear Ordering is the problem of finding a linear order of the nodes of a graph such that the sum of the weights which are consistent with this order is as large as possible. It is an NP - Hard combinatorial optimisation ...

Linear programming based on neural networks for radiotherapy treatment planning

International Nuclear Information System (INIS)

Xingen Wu; Limin Luo

2000-01-01

In this paper, we propose a neural network model for linear programming that is designed to optimize radiotherapy treatment planning (RTP). This kind of neural network can be easily implemented by using a kind of 'neural' electronic system in order to obtain an optimization solution in real time. We first give an introduction to the RTP problem and construct a non-constraint objective function for the neural network model. We adopt a gradient algorithm to minimize the objective function and design the structure of the neural network for RTP. Compared to traditional linear programming methods, this neural network model can reduce the time needed for convergence, the size of problems (i.e., the number of variables to be searched) and the number of extra slack and surplus variables needed. We obtained a set of optimized beam weights that result in a better dose distribution as compared to that obtained using the simplex algorithm under the same initial condition. The example presented in this paper shows that this model is feasible in three-dimensional RTP. (author)

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...

A duality approach for solving bounded linear programming problems with fuzzy variables based on ranking functions and its application in bounded transportation problems

Science.gov (United States)

Ebrahimnejad, Ali

2015-08-01

There are several methods, in the literature, for solving fuzzy variable linear programming problems (fuzzy linear programming in which the right-hand-side vectors and decision variables are represented by trapezoidal fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings a new method based on the bounded dual simplex method is proposed to determine the fuzzy optimal solution of that kind of fuzzy variable linear programming problems in which some or all variables are restricted to lie within lower and upper bounds. To illustrate the proposed method, an application example is solved and the obtained results are given. The advantages of the proposed method over existing methods are discussed. Also, one application of this algorithm in solving bounded transportation problems with fuzzy supplies and demands is dealt with. The proposed method is easy to understand and to apply for determining the fuzzy optimal solution of bounded fuzzy variable linear programming problems occurring in real-life situations.

Periodic solutions of asymptotically linear Hamiltonian systems without twist conditions

Energy Technology Data Exchange (ETDEWEB)

Cheng Rong [Coll. of Mathematics and Physics, Nanjing Univ. of Information Science and Tech., Nanjing (China); Dept. of Mathematics, Southeast Univ., Nanjing (China); Zhang Dongfeng [Dept. of Mathematics, Southeast Univ., Nanjing (China)

2010-05-15

In dynamical system theory, especially in many fields of applications from mechanics, Hamiltonian systems play an important role, since many related equations in mechanics can be written in an Hamiltonian form. In this paper, we study the existence of periodic solutions for a class of Hamiltonian systems. By applying the Galerkin approximation method together with a result of critical point theory, we establish the existence of periodic solutions of asymptotically linear Hamiltonian systems without twist conditions. Twist conditions play crucial roles in the study of periodic solutions for asymptotically linear Hamiltonian systems. The lack of twist conditions brings some difficulty to the study. To the authors' knowledge, very little is known about the case, where twist conditions do not hold. (orig.)

An Instructional Note on Linear Programming--A Pedagogically Sound Approach.

Science.gov (United States)

Mitchell, Richard

1998-01-01

Discusses the place of linear programming in college curricula and the advantages of using linear-programming software. Lists important characteristics of computer software used in linear programming for more effective teaching and learning. (ASK)

Some problems on non-linear semigroups and the blow-up of integral solutions

International Nuclear Information System (INIS)

Pavel, N.H.

1983-07-01

After some introductory remarks, this highly mathematical document considers a unifying approach in the theory of non-linear semigroups. Then a brief survey is given on blow-up of mild solutions from the semilinear case. Finally, the global behavior of solutions to non-linear evolution equations is addressed; it is found that classical results on the behavior of the maximal solution u as t up-arrow tsub(max) hold also for integral solutions

A new neural network model for solving random interval linear programming problems.

Science.gov (United States)

Arjmandzadeh, Ziba; Safi, Mohammadreza; Nazemi, Alireza

2017-05-01

This paper presents a neural network model for solving random interval linear programming problems. The original problem involving random interval variable coefficients is first transformed into an equivalent convex second order cone programming problem. A neural network model is then constructed for solving the obtained convex second order cone problem. Employing Lyapunov function approach, it is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact satisfactory solution of the original problem. Several illustrative examples are solved in support of this technique. Copyright © 2017 Elsevier Ltd. All rights reserved.

POSITIVE SOLUTIONS TO SEMI-LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACE

Institute of Scientific and Technical Information of China (English)

无

2008-01-01

In this paper,we study the existence of positive periodic solution to some second- order semi-linear differential equation in Banach space.By the fixed point index theory, we prove that the semi-linear differential equation has two positive periodic solutions.

Joint shape segmentation with linear programming

KAUST Repository

Huang, Qixing; Koltun, Vladlen; Guibas, Leonidas

2011-01-01

program is solved via a linear programming relaxation, using a block coordinate descent procedure that makes the optimization feasible for large databases. We evaluate the presented approach on the Princeton segmentation benchmark and show that joint shape

Robust Stability and H∞ Control of Uncertain Piecewise Linear Switched Systems with Filippov Solutions

DEFF Research Database (Denmark)

Ahmadi, Mohamadreza; Mojallali, Hamed; Wisniewski, Rafal

2012-01-01

This paper addresses the robust stability and control problem of uncertain piecewise linear switched systems where, instead of the conventional Carathe ́odory solutions, we allow for Filippov solutions. In other words, in contrast to the previous studies, solutions with infinite switching in fini...... algorithm is proposed to surmount the aforementioned matrix inequality conditions....... time along the facets and on faces of arbitrary dimensions are also taken into account. Firstly, based on earlier results, the stability problem of piecewise linear systems with Filippov solutions is translated into a number of linear matrix inequality feasibility tests. Subsequently, a set of matrix...... inequalities are brought forward, which determines the asymptotic stability of the Filippov solutions of a given uncertain piecewise linear system. Afterwards, bilinear matrix inequality conditions for synthesizing a robust controller with a guaranteed H∞ per- formance are formulated. Finally, a V-K iteration...

Solutions of the linearized Bach-Einstein equation in the static spherically symmetric case

International Nuclear Information System (INIS)

Schmidt, H.J.

1985-01-01

The Bach-Einstein equation linearized around Minkowski space-time is completely solved. The set of solutions depends on three parameters; a two-parameter subset of it becomes asymptotically flat. In that region the gravitational potential is of the type phi = -m/r + epsilon exp (-r/l). Because of the different asymptotic behaviour of both terms, it became necessary to linearize also around the Schwarzschild solution phi = -m/r. The linearized equation resulting in this case is discussed using qualitative methods. The result is that for m = 2l phi = -m/r + epsilon r -2 exp (-r/l) u, where u is some bounded function; m is arbitrary and epsilon again small. Further, the relation between the solution of the linearized and the full equation is discussed. (author)

Towards lexicographic multi-objective linear programming using grossone methodology

Science.gov (United States)

Cococcioni, Marco; Pappalardo, Massimo; Sergeyev, Yaroslav D.

2016-10-01

Lexicographic Multi-Objective Linear Programming (LMOLP) problems can be solved in two ways: preemptive and nonpreemptive. The preemptive approach requires the solution of a series of LP problems, with changing constraints (each time the next objective is added, a new constraint appears). The nonpreemptive approach is based on a scalarization of the multiple objectives into a single-objective linear function by a weighted combination of the given objectives. It requires the specification of a set of weights, which is not straightforward and can be time consuming. In this work we present both mathematical and software ingredients necessary to solve LMOLP problems using a recently introduced computational methodology (allowing one to work numerically with infinities and infinitesimals) based on the concept of grossone. The ultimate goal of such an attempt is an implementation of a simplex-like algorithm, able to solve the original LMOLP problem by solving only one single-objective problem and without the need to specify finite weights. The expected advantages are therefore obvious.

A Fuzzy Linear Programming Approach for Aggregate Production Planning

DEFF Research Database (Denmark)

Iris, Cagatay; Cevikcan, Emre

2014-01-01

a mathematical programming framework for aggregate production planning problem under imprecise data environment. After providing background information about APP problem, together with fuzzy linear programming, the fuzzy linear programming model of APP is solved on an illustrative example for different a...

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.

A recurrent neural network for solving bilevel linear programming problem.

Science.gov (United States)

He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie; Huang, Junjian

2014-04-01

In this brief, based on the method of penalty functions, a recurrent neural network (NN) modeled by means of a differential inclusion is proposed for solving the bilevel linear programming problem (BLPP). Compared with the existing NNs for BLPP, the model has the least number of state variables and simple structure. Using nonsmooth analysis, the theory of differential inclusions, and Lyapunov-like method, the equilibrium point sequence of the proposed NNs can approximately converge to an optimal solution of BLPP under certain conditions. Finally, the numerical simulations of a supply chain distribution model have shown excellent performance of the proposed recurrent NNs.

EABOT - Energetic analysis as a basis for robust optimization of trigeneration systems by linear programming

International Nuclear Information System (INIS)

Piacentino, A.; Cardona, F.

2008-01-01

The optimization of synthesis, design and operation in trigeneration systems for building applications is a quite complex task, due to the high number of decision variables, the presence of irregular heat, cooling and electric load profiles and the variable electricity price. Consequently, computer-aided techniques are usually adopted to achieve the optimal solution, based either on iterative techniques, linear or non-linear programming or evolutionary search. Large efforts have been made in improving algorithm efficiency, which have resulted in an increasingly rapid convergence to the optimal solution and in reduced calculation time; robust algorithm have also been formulated, assuming stochastic behaviour for energy loads and prices. This paper is based on the assumption that margins for improvements in the optimization of trigeneration systems still exist, which require an in-depth understanding of plant's energetic behaviour. Robustness in the optimization of trigeneration systems has more to do with a 'correct and comprehensive' than with an 'efficient' modelling, being larger efforts required to energy specialists rather than to experts in efficient algorithms. With reference to a mixed integer linear programming model implemented in MatLab for a trigeneration system including a pressurized (medium temperature) heat storage, the relevant contribute of thermoeconomics and energo-environmental analysis in the phase of mathematical modelling and code testing are shown

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.

The use of linear programming in optimization of HDR implant dose distributions

International Nuclear Information System (INIS)

Jozsef, Gabor; Streeter, Oscar E.; Astrahan, Melvin A.

2003-01-01

The introduction of high dose rate brachytherapy enabled optimization of dose distributions to be used on a routine basis. The objective of optimization is to homogenize the dose distribution within the implant while simultaneously satisfying dose constraints on certain points. This is accomplished by varying the time the source dwells at different locations. As the dose at any point is a linear function of the dwell times, a linear programming approach seems to be a natural choice. The dose constraints are inherently linear inequalities. Homogeneity requirements are linearized by minimizing the maximum deviation of the doses at points inside the implant from a prescribed dose. The revised simplex method was applied for the solution of this linear programming problem. In the homogenization process the possible source locations were chosen as optimization points. To avoid the problem of the singular value of the dose at a source location from the source itself we define the 'self-contribution' as the dose at a small distance from the source. The effect of varying this distance is discussed. Test cases were optimized for planar, biplanar and cylindrical implants. A semi-irregular, fan-like implant with diverging needles was also investigated. Mean central dose calculation based on 3D Delaunay-triangulation of the source locations was used to evaluate the dose distributions. The optimization method resulted in homogeneous distributions (for brachytherapy). Additional dose constraints--when applied--were satisfied. The method is flexible enough to include other linear constraints such as the inclusion of the centroids of the Delaunay-triangulation for homogenization, or limiting the maximum allowable dwell time

On the exactness of the cavity method for weighted b-matchings on arbitrary graphs and its relation to linear programs

International Nuclear Information System (INIS)

Bayati, Mohsen; Borgs, Christian; Chayes, Jennifer; Zecchina, Riccardo

2008-01-01

We consider the general problem of finding the minimum weight b-matching on arbitrary graphs. We prove that, whenever the linear programing relaxation of the problem has no fractional solutions, then the cavity or belief propagation equations converge to the correct solution both for synchronous and asynchronous updating. (letter)

Game Theory and its Relationship with Linear Programming Models ...

African Journals Online (AJOL)

Game Theory and its Relationship with Linear Programming Models. ... This paper shows that game theory and linear programming problem are closely related subjects since any computing method devised for ... AJOL African Journals Online.

An Efficacious Multi-Objective Fuzzy Linear Programming Approach for Optimal Power Flow Considering Distributed Generation.

Science.gov (United States)

Warid, Warid; Hizam, Hashim; Mariun, Norman; Abdul-Wahab, Noor Izzri

2016-01-01

This paper proposes a new formulation for the multi-objective optimal power flow (MOOPF) problem for meshed power networks considering distributed generation. An efficacious multi-objective fuzzy linear programming optimization (MFLP) algorithm is proposed to solve the aforementioned problem with and without considering the distributed generation (DG) effect. A variant combination of objectives is considered for simultaneous optimization, including power loss, voltage stability, and shunt capacitors MVAR reserve. Fuzzy membership functions for these objectives are designed with extreme targets, whereas the inequality constraints are treated as hard constraints. The multi-objective fuzzy optimal power flow (OPF) formulation was converted into a crisp OPF in a successive linear programming (SLP) framework and solved using an efficient interior point method (IPM). To test the efficacy of the proposed approach, simulations are performed on the IEEE 30-busand IEEE 118-bus test systems. The MFLP optimization is solved for several optimization cases. The obtained results are compared with those presented in the literature. A unique solution with a high satisfaction for the assigned targets is gained. Results demonstrate the effectiveness of the proposed MFLP technique in terms of solution optimality and rapid convergence. Moreover, the results indicate that using the optimal DG location with the MFLP algorithm provides the solution with the highest quality.

Some examples of non-linear systems and characteristics of their solutions

CSIR Research Space (South Africa)

Greben, JM

2006-07-01

Full Text Available . In contrast to certain other applications in complexity theory, these non-linear solutions are characterized by great stability. To go beyond the dominant non-perturbative solution one has to consider the source term as well. The parameter freedom...

Optimal traffic control in highway transportation networks using linear programming

KAUST Repository

Li, Yanning

2014-06-01

This article presents a framework for the optimal control of boundary flows on transportation networks. The state of the system is modeled by a first order scalar conservation law (Lighthill-Whitham-Richards PDE). Based on an equivalent formulation of the Hamilton-Jacobi PDE, the problem of controlling the state of the system on a network link in a finite horizon can be posed as a Linear Program. Assuming all intersections in the network are controllable, we show that the optimization approach can be extended to an arbitrary transportation network, preserving linear constraints. Unlike previously investigated transportation network control schemes, this framework leverages the intrinsic properties of the Halmilton-Jacobi equation, and does not require any discretization or boolean variables on the link. Hence this framework is very computational efficient and provides the globally optimal solution. The feasibility of this framework is illustrated by an on-ramp metering control example.

Linearized Programming of Memristors for Artificial Neuro-Sensor Signal Processing.

Science.gov (United States)

Yang, Changju; Kim, Hyongsuk

2016-08-19

A linearized programming method of memristor-based neural weights is proposed. Memristor is known as an ideal element to implement a neural synapse due to its embedded functions of analog memory and analog multiplication. Its resistance variation with a voltage input is generally a nonlinear function of time. Linearization of memristance variation about time is very important for the easiness of memristor programming. In this paper, a method utilizing an anti-serial architecture for linear programming is proposed. The anti-serial architecture is composed of two memristors with opposite polarities. It linearizes the variation of memristance due to complimentary actions of two memristors. For programming a memristor, additional memristor with opposite polarity is employed. The linearization effect of weight programming of an anti-serial architecture is investigated and memristor bridge synapse which is built with two sets of anti-serial memristor architecture is taken as an application example of the proposed method. Simulations are performed with memristors of both linear drift model and nonlinear model.

Preprocessing in Matlab Inconsistent Linear System for a Meaningful Least Squares Solution

Science.gov (United States)

Sen, Symal K.; Shaykhian, Gholam Ali

2011-01-01

Mathematical models of many physical/statistical problems are systems of linear equations Due to measurement and possible human errors/mistakes in modeling/data, as well as due to certain assumptions to reduce complexity, inconsistency (contradiction) is injected into the model, viz. the linear system. While any inconsistent system irrespective of the degree of inconsistency has always a least-squares solution, one needs to check whether an equation is too much inconsistent or, equivalently too much contradictory. Such an equation will affect/distort the least-squares solution to such an extent that renders it unacceptable/unfit to be used in a real-world application. We propose an algorithm which (i) prunes numerically redundant linear equations from the system as these do not add any new information to the model, (ii) detects contradictory linear equations along with their degree of contradiction (inconsistency index), (iii) removes those equations presumed to be too contradictory, and then (iv) obtain the . minimum norm least-squares solution of the acceptably inconsistent reduced linear system. The algorithm presented in Matlab reduces the computational and storage complexities and also improves the accuracy of the solution. It also provides the necessary warning about the existence of too much contradiction in the model. In addition, we suggest a thorough relook into the mathematical modeling to determine the reason why unacceptable contradiction has occurred thus prompting us to make necessary corrections/modifications to the models - both mathematical and, if necessary, physical.

Solution methods for large systems of linear equations in BACCHUS

International Nuclear Information System (INIS)

Homann, C.; Dorr, B.

1993-05-01

The computer programme BACCHUS is used to describe steady state and transient thermal-hydraulic behaviour of a coolant in a fuel element with intact geometry in a fast breeder reactor. In such computer programmes generally large systems of linear equations with sparse matrices of coefficients, resulting from discretization of coolant conservation equations, must be solved thousands of times giving rise to large demands of main storage and CPU time. Direct and iterative solution methods of the systems of linear equations, available in BACCHUS, are described, giving theoretical details and experience with their use in the programme. Besides use of a method of lines, a Runge-Kutta-method, for solution of the partial differential equation is outlined. (orig.) [de

Inverse scattering solution of non-linear evolution equations in one space dimension: an introduction

International Nuclear Information System (INIS)

Alvarez-Estrada, R.F.

1979-01-01

A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly

Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series

Science.gov (United States)

Gnoffo, Peter A.

2015-01-01

Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.

Evaluation of film dosemeters by linear programming

International Nuclear Information System (INIS)

Kragh, P.; Nitschke, J.

1992-01-01

An evaluation method for multi-component dosemeters is described which uses linear programming in order to decrease the dependence on energy and direction. The results of this method are more accurate than those obtained with the evaluation methods so far applied in film dosimetry. In addition, systematic errors can be given when evaluating individual measurements. Combined linear programming, as a special case of the presented method, is described taking a film dosemeter of particular type as an example. (orig.) [de

Exact solution to the Coulomb wave using the linearized phase-amplitude method

Directory of Open Access Journals (Sweden)

Shuji Kiyokawa

2015-08-01

Full Text Available The author shows that the amplitude equation from the phase-amplitude method of calculating continuum wave functions can be linearized into a 3rd-order differential equation. Using this linearized equation, in the case of the Coulomb potential, the author also shows that the amplitude function has an analytically exact solution represented by means of an irregular confluent hypergeometric function. Furthermore, it is shown that the exact solution for the Coulomb potential reproduces the wave function for free space expressed by the spherical Bessel function. The amplitude equation for the large component of the Dirac spinor is also shown to be the linearized 3rd-order differential equation.

Minimal solution of linear formed fuzzy matrix equations

Directory of Open Access Journals (Sweden)

Maryam Mosleh

2012-10-01

Full Text Available In this paper according to the structured element method, the $mimes n$ inconsistent fuzzy matrix equation $Ailde{X}=ilde{B},$ which are linear formed by fuzzy structured element, is investigated. The necessary and sufficient condition for the existence of a fuzzy solution is also discussed. some examples are presented to illustrate the proposed method.

Focal points and principal solutions of linear Hamiltonian systems revisited

Science.gov (United States)

Šepitka, Peter; Šimon Hilscher, Roman

2018-05-01

In this paper we present a novel view on the principal (and antiprincipal) solutions of linear Hamiltonian systems, as well as on the focal points of their conjoined bases. We present a new and unified theory of principal (and antiprincipal) solutions at a finite point and at infinity, and apply it to obtain new representation of the multiplicities of right and left proper focal points of conjoined bases. We show that these multiplicities can be characterized by the abnormality of the system in a neighborhood of the given point and by the rank of the associated T-matrix from the theory of principal (and antiprincipal) solutions. We also derive some additional important results concerning the representation of T-matrices and associated normalized conjoined bases. The results in this paper are new even for completely controllable linear Hamiltonian systems. We also discuss other potential applications of our main results, in particular in the singular Sturmian theory.

Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

Directory of Open Access Journals (Sweden)

Hamidreza Rezazadeh

2014-05-01

Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.

Asymptotic solutions and spectral theory of linear wave equations

International Nuclear Information System (INIS)

Adam, J.A.

1982-01-01

This review contains two closely related strands. Firstly the asymptotic solution of systems of linear partial differential equations is discussed, with particular reference to Lighthill's method for obtaining the asymptotic functional form of the solution of a scalar wave equation with constant coefficients. Many of the applications of this technique are highlighted. Secondly, the methods and applications of the theory of the reduced (one-dimensional) wave equation - particularly spectral theory - are discussed. While the breadth of application and power of the techniques is emphasised throughout, the opportunity is taken to present to a wider readership, developments of the methods which have occured in some aspects of astrophysical (particularly solar) and geophysical fluid dynamics. It is believed that the topics contained herein may be of relevance to the applied mathematician or theoretical physicist interest in problems of linear wave propagation in these areas. (orig./HSI)

About simple nonlinear and linear superpositions of special exact solutions of Veselov-Novikov equation

International Nuclear Information System (INIS)

Dubrovsky, V. G.; Topovsky, A. V.

2013-01-01

New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u (n) , n= 1, …, N are constructed via Zakharov and Manakov ∂-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u (n) and calculated by ∂-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schrödinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u (n) . It is shown that the sums u=u (k 1 ) +...+u (k m ) , 1 ⩽k 1 2 m ⩽N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schrödinger equation and can serve as model potentials for electrons in planar structures of modern electronics.

Optimization Research of Generation Investment Based on Linear Programming Model

Science.gov (United States)

Wu, Juan; Ge, Xueqian

Linear programming is an important branch of operational research and it is a mathematical method to assist the people to carry out scientific management. GAMS is an advanced simulation and optimization modeling language and it will combine a large number of complex mathematical programming, such as linear programming LP, nonlinear programming NLP, MIP and other mixed-integer programming with the system simulation. In this paper, based on the linear programming model, the optimized investment decision-making of generation is simulated and analyzed. At last, the optimal installed capacity of power plants and the final total cost are got, which provides the rational decision-making basis for optimized investments.

Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

Science.gov (United States)

El-Gebeily, M.; Yushau, B.

2008-01-01

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

A Sawmill Manager Adapts To Change With Linear Programming

Science.gov (United States)

George F. Dutrow; James E. Granskog

1973-01-01

Linear programming provides guidelines for increasing sawmill capacity and flexibility and for determining stumpagepurchasing strategy. The operator of a medium-sized sawmill implemented improvements suggested by linear programming analysis; results indicate a 45 percent increase in revenue and a 36 percent hike in volume processed.

Analytical solution for a linearly graded-index-profile planar waveguide.

Science.gov (United States)

Touam, T; Yergeau, F

1993-01-20

An analytical solution is presented for the TE modes of a planar waveguide structure comprising a high-index guiding layer and a buried layer with a profile such that the square of the index varies linearly and matches the substrate and high-index guiding layer. The electric-field profiles and the dispersion relation are obtained and discussed, and a solution by the WKB method is compared.

175 Years of Linear Programming

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 10. 175 Years of Linear Programming - Max Flow = Min Cut. Vijay Chandru M R Rao. Series Article Volume 4 Issue 10 October 1999 pp 22-39. Fulltext. Click here to view fulltext PDF. Permanent link:

175 Years of Linear Programming

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 5. 175 Years of Linear Programming - Pune's Gift. Vijay Chandru M R Rao. Series Article Volume 4 Issue 5 May ... Computer Science and Automation, IISc Bangalore 560012, India. Director, Indian Institute of Management, Bannerghatta Road, ...

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 ...

Improved harmonic balance approach to periodic solutions of non-linear jerk equations

International Nuclear Information System (INIS)

Wu, B.S.; Lim, C.W.; Sun, W.P.

2006-01-01

An analytical approximate approach for determining periodic solutions of non-linear jerk equations involving third-order time-derivative is presented. This approach incorporates salient features of both Newton's method and the method of harmonic balance. By appropriately imposing the method of harmonic balance to the linearized equation, the approach requires only one or two iterations to predict very accurate analytical approximate solutions for a large range of initial velocity amplitude. One typical example is used to verify and illustrate the usefulness and effectiveness of the proposed approach

Portfolio selection problem: a comparison of fuzzy goal programming and linear physical programming

Directory of Open Access Journals (Sweden)

Fusun Kucukbay

2016-04-01

Full Text Available Investors have limited budget and they try to maximize their return with minimum risk. Therefore this study aims to deal with the portfolio selection problem. In the study two criteria are considered which are expected return, and risk. In this respect, linear physical programming (LPP technique is applied on Bist 100 stocks to be able to find out the optimum portfolio. The analysis covers the period April 2009- March 2015. This period is divided into two; April 2009-March 2014 and April 2014 – March 2015. April 2009-March 2014 period is used as data to find an optimal solution. April 2014-March 2015 period is used to test the real performance of portfolios. The performance of the obtained portfolio is compared with that obtained from fuzzy goal programming (FGP. Then the performances of both method, LPP and FGP are compared with BIST 100 in terms of their Sharpe Indexes. The findings reveal that LPP for portfolio selection problem is a good alternative to FGP.

Using Set Covering with Item Sampling to Analyze the Infeasibility of Linear Programming Test Assembly Models

Science.gov (United States)

Huitzing, Hiddo A.

2004-01-01

This article shows how set covering with item sampling (SCIS) methods can be used in the analysis and preanalysis of linear programming models for test assembly (LPTA). LPTA models can construct tests, fulfilling a set of constraints set by the test assembler. Sometimes, no solution to the LPTA model exists. The model is then said to be…

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.

Asymptotic formulae for solutions of half-linear differential equations

Czech Academy of Sciences Publication Activity Database

Řehák, Pavel

2017-01-01

Roč. 292, January (2017), s. 165-177 ISSN 0096-3003 Institutional support: RVO:67985840 Keywords : half-linear differential equation * nonoscillatory solution * regular variation Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.738, year: 2016 http://www.sciencedirect.com/science/article/pii/S0096300316304581

A generalized fuzzy credibility-constrained linear fractional programming approach for optimal irrigation water allocation under uncertainty

Science.gov (United States)

Zhang, Chenglong; Guo, Ping

2017-10-01

The vague and fuzzy parametric information is a challenging issue in irrigation water management problems. In response to this problem, a generalized fuzzy credibility-constrained linear fractional programming (GFCCFP) model is developed for optimal irrigation water allocation under uncertainty. The model can be derived from integrating generalized fuzzy credibility-constrained programming (GFCCP) into a linear fractional programming (LFP) optimization framework. Therefore, it can solve ratio optimization problems associated with fuzzy parameters, and examine the variation of results under different credibility levels and weight coefficients of possibility and necessary. It has advantages in: (1) balancing the economic and resources objectives directly; (2) analyzing system efficiency; (3) generating more flexible decision solutions by giving different credibility levels and weight coefficients of possibility and (4) supporting in-depth analysis of the interrelationships among system efficiency, credibility level and weight coefficient. The model is applied to a case study of irrigation water allocation in the middle reaches of Heihe River Basin, northwest China. Therefore, optimal irrigation water allocation solutions from the GFCCFP model can be obtained. Moreover, factorial analysis on the two parameters (i.e. λ and γ) indicates that the weight coefficient is a main factor compared with credibility level for system efficiency. These results can be effective for support reasonable irrigation water resources management and agricultural production.

Analytic central path, sensitivity analysis and parametric linear programming

NARCIS (Netherlands)

A.G. Holder; J.F. Sturm; S. Zhang (Shuzhong)

1998-01-01

textabstractIn this paper we consider properties of the central path and the analytic center of the optimal face in the context of parametric linear programming. We first show that if the right-hand side vector of a standard linear program is perturbed, then the analytic center of the optimal face

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

An improved exploratory search technique for pure integer linear programming problems

Science.gov (United States)

Fogle, F. R.

1990-01-01

The development is documented of a heuristic method for the solution of pure integer linear programming problems. The procedure draws its methodology from the ideas of Hooke and Jeeves type 1 and 2 exploratory searches, greedy procedures, and neighborhood searches. It uses an efficient rounding method to obtain its first feasible integer point from the optimal continuous solution obtained via the simplex method. Since this method is based entirely on simple addition or subtraction of one to each variable of a point in n-space and the subsequent comparison of candidate solutions to a given set of constraints, it facilitates significant complexity improvements over existing techniques. It also obtains the same optimal solution found by the branch-and-bound technique in 44 of 45 small to moderate size test problems. Two example problems are worked in detail to show the inner workings of the method. Furthermore, using an established weighted scheme for comparing computational effort involved in an algorithm, a comparison of this algorithm is made to the more established and rigorous branch-and-bound method. A computer implementation of the procedure, in PC compatible Pascal, is also presented and discussed.

Application of mixed-integer linear programming in a car seats assembling process

Directory of Open Access Journals (Sweden)

Jorge Iván Perez Rave

2011-12-01

Full Text Available In this paper, a decision problem involving a car parts manufacturing company is modeled in order to prepare the company for an increase in demand. Mixed-integer linear programming was used with the following decision variables: creating a second shift, purchasing additional equipment, determining the required work force, and other alternatives involving new manners of work distribution that make it possible to separate certain operations from some workplaces and integrate them into others to minimize production costs. The model was solved using GAMS. The solution consisted of programming 19 workers under a configuration that merges two workplaces and separates some operations from some workplaces. The solution did not involve purchasing additional machinery or creating a second shift. As a result, the manufacturing paradigms that had been valid in the company for over 14 years were broken. This study allowed the company to increase its productivity and obtain significant savings. It also shows the benefits of joint work between academia and companies, and provides useful information for professors, students and engineers regarding production and continuous improvement.

Very Low-Cost Nutritious Diet Plans Designed by Linear Programming.

Science.gov (United States)

Foytik, Jerry

1981-01-01

Provides procedural details of Linear Programing, developed by the U.S. Department of Agriculture to devise a dietary guide for consumers that minimizes food costs without sacrificing nutritional quality. Compares Linear Programming with the Thrifty Food Plan, which has been a basis for allocating coupons under the Food Stamp Program. (CS)

Updating Linear Schedules with Lowest Cost: a Linear Programming Model

Science.gov (United States)

Biruk, Sławomir; Jaśkowski, Piotr; Czarnigowska, Agata

2017-10-01

Many civil engineering projects involve sets of tasks repeated in a predefined sequence in a number of work areas along a particular route. A useful graphical representation of schedules of such projects is time-distance diagrams that clearly show what process is conducted at a particular point of time and in particular location. With repetitive tasks, the quality of project performance is conditioned by the ability of the planner to optimize workflow by synchronizing the works and resources, which usually means that resources are planned to be continuously utilized. However, construction processes are prone to risks, and a fully synchronized schedule may expire if a disturbance (bad weather, machine failure etc.) affects even one task. In such cases, works need to be rescheduled, and another optimal schedule should be built for the changed circumstances. This typically means that, to meet the fixed completion date, durations of operations have to be reduced. A number of measures are possible to achieve such reduction: working overtime, employing more resources or relocating resources from less to more critical tasks, but they all come at a considerable cost and affect the whole project. The paper investigates the problem of selecting the measures that reduce durations of tasks of a linear project so that the cost of these measures is kept to the minimum and proposes an algorithm that could be applied to find optimal solutions as the need to reschedule arises. Considering that civil engineering projects, such as road building, usually involve less process types than construction projects, the complexity of scheduling problems is lower, and precise optimization algorithms can be applied. Therefore, the authors put forward a linear programming model of the problem and illustrate its principle of operation with an example.

Non-monotone positive solutions of second-order linear differential equations: existence, nonexistence and criteria

Directory of Open Access Journals (Sweden)

Mervan Pašić

2016-10-01

Full Text Available We study non-monotone positive solutions of the second-order linear differential equations: $(p(tx'' + q(t x = e(t$, with positive $p(t$ and $q(t$. For the first time, some criteria as well as the existence and nonexistence of non-monotone positive solutions are proved in the framework of some properties of solutions $\\theta (t$ of the corresponding integrable linear equation: $(p(t\\theta''=e(t$. The main results are illustrated by many examples dealing with equations which allow exact non-monotone positive solutions not necessarily periodic. Finally, we pose some open questions.

Exact solution of some linear matrix equations using algebraic methods

Science.gov (United States)

Djaferis, T. E.; Mitter, S. K.

1977-01-01

A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.

About simple nonlinear and linear superpositions of special exact solutions of Veselov-Novikov equation

Energy Technology Data Exchange (ETDEWEB)

Dubrovsky, V. G.; Topovsky, A. V. [Novosibirsk State Technical University, Karl Marx prosp. 20, Novosibirsk 630092 (Russian Federation)

2013-03-15

New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u{sup (n)}, n= 1, Horizontal-Ellipsis , N are constructed via Zakharov and Manakov {partial_derivative}-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u{sup (n)} and calculated by {partial_derivative}-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schroedinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u{sup (n)}. It is shown that the sums u=u{sup (k{sub 1})}+...+u{sup (k{sub m})}, 1 Less-Than-Or-Slanted-Equal-To k{sub 1} < k{sub 2} < Horizontal-Ellipsis < k{sub m} Less-Than-Or-Slanted-Equal-To N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schroedinger equation and can serve as model potentials for electrons in planar structures of modern electronics.

Knotted solutions for linear and nonlinear theories: Electromagnetism and fluid dynamics

Directory of Open Access Journals (Sweden)

Daniel W.F. Alves

2017-10-01

Full Text Available We examine knotted solutions, the most simple of which is the “Hopfion”, from the point of view of relations between electromagnetism and ideal fluid dynamics. A map between fluid dynamics and electromagnetism works for initial conditions or for linear perturbations, allowing us to find new knotted fluid solutions. Knotted solutions are also found to be solutions of nonlinear generalizations of electromagnetism, and of quantum-corrected actions for electromagnetism coupled to other modes. For null configurations, electromagnetism can be described as a null pressureless fluid, for which we can find solutions from the knotted solutions of electromagnetism. We also map them to solutions of Euler's equations, obtained from a type of nonrelativistic reduction of the relativistic fluid equations.

On nonnegative solutions of second order linear functional differential equations

Czech Academy of Sciences Publication Activity Database

Lomtatidze, Alexander; Vodstrčil, Petr

2004-01-01

Roč. 32, č. 1 (2004), s. 59-88 ISSN 1512-0015 Institutional research plan: CEZ:AV0Z1019905 Keywords : second order linear functional differential equations * nonnegative solution * two-point boundary value problem Subject RIV: BA - General Mathematics

The Quasi-Linear Solution of Vertical Infiltration; La solucion cuasi-lineal de la infiltracion vertical

Energy Technology Data Exchange (ETDEWEB)

Fuentes, Carlos [Instituto Mexicano de Tecnologia del Agua, Jiutepec, Morelos (Mexico); Parlangue, Jean-Yves [Departamento de Agricultura e Ingenieria Biologica (United States); Haverkamp, Randel; Vauclin, Michael [Laboratorio de Estudio de las Transferencias en Hidrologia y Medio ambiente (France)

2001-12-01

The exact solution of the one-dimensional vertical infiltration equation is deducted, when the hydraulic diffusivity is considered constant and the hydraulic conductivity is a combination of both a linear and quadratic functions of the soil water content. This quasi-linear solution includes as particular cases, both the classical solution known as linear soil and the Knight solution. The cumulative infiltrated water as a function of time provided by the quasi-linear solution has been compared with the cumulative infiltrated water obtained from the numerical solution of the Richards equation on three different soils of contrasting hydrodynamic properties. The good agreement between the two solutions has shown that the quasi-linear solution can be used on soils where the accepted hypothesis, on hydraulic diffusivity and hydraulic conductivity, for its deduction is not satisfied. [Spanish] Se deduce la solucion exacta de la ecuacion de la infiltracion unidimensional vertical cuando la difusividad hidraulica es considerada constante y la conductividad hidraulica es una combinacion de una funcion lineal y una cuadratica del contenido volumetrico de agua. Esta solucion cuasi-lineal de la infiltracion contiene, como casos particulares, la solucion clasica conocida como suelo lineal y la solucion de Knight. La lamina infiltrada acumulada en funcion del tiempo proporcionada por la solucion cuasi-lineal se ha comparado con la lamina infiltrada proporcionada por la solucion numerica de la ecuacion de Richards en tres suelos de propiedades hidrodinamicas contrastantes. El buen acuerdo entre las laminas infiltradas ha mostrado que la solucion cuasi-lineal puede utilizarse en suelos donde la difusividad y la conductividad hidraulicas no satisfacen los supuestos de la deduccion.

An Interval-Parameter Fuzzy Linear Programming with Stochastic Vertices Model for Water Resources Management under Uncertainty

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Yan Han

2013-01-01

Full Text Available An interval-parameter fuzzy linear programming with stochastic vertices (IFLPSV method is developed for water resources management under uncertainty by coupling interval-parameter fuzzy linear programming (IFLP with stochastic programming (SP. As an extension of existing interval parameter fuzzy linear programming, the developed IFLPSV approach has advantages in dealing with dual uncertainty optimization problems, which uncertainty presents as interval parameter with stochastic vertices in both of the objective functions and constraints. The developed IFLPSV method improves upon the IFLP method by allowing dual uncertainty parameters to be incorporated into the optimization processes. A hybrid intelligent algorithm based on genetic algorithm and artificial neural network is used to solve the developed model. The developed method is then applied to water resources allocation in Beijing city of China in 2020, where water resources shortage is a challenging issue. The results indicate that reasonable solutions have been obtained, which are helpful and useful for decision makers. Although the amount of water supply from Guanting and Miyun reservoirs is declining with rainfall reduction, water supply from the South-to-North Water Transfer project will have important impact on water supply structure of Beijing city, particularly in dry year and extraordinary dry year.

Iterative solution of linear equations in ODE codes. [Krylov subspaces

Energy Technology Data Exchange (ETDEWEB)

Gear, C. W.; Saad, Y.

1981-01-01

Each integration step of a stiff equation involves the solution of a nonlinear equation, usually by a quasi-Newton method that leads to a set of linear problems. Iterative methods for these linear equations are studied. Of particular interest are methods that do not require an explicit Jacobian, but can work directly with differences of function values using J congruent to f(x + delta) - f(x). Some numerical experiments using a modification of LSODE are reported. 1 figure, 2 tables.

An easy way to obtain strong duality results in linear, linear semidefinite and linear semi-infinite programming

NARCIS (Netherlands)

Pop, P.C.; Still, Georg J.

1999-01-01

In linear programming it is known that an appropriate non-homogeneous Farkas Lemma leads to a short proof of the strong duality results for a pair of primal and dual programs. By using a corresponding generalized Farkas lemma we give a similar proof of the strong duality results for semidefinite

The simplex method of linear programming

CERN Document Server

Ficken, Frederick A

1961-01-01

This concise but detailed and thorough treatment discusses the rudiments of the well-known simplex method for solving optimization problems in linear programming. Geared toward undergraduate students, the approach offers sufficient material for readers without a strong background in linear algebra. Many different kinds of problems further enrich the presentation. The text begins with examinations of the allocation problem, matrix notation for dual problems, feasibility, and theorems on duality and existence. Subsequent chapters address convex sets and boundedness, the prepared problem and boun

Block level energy planning for domestic lighting - a multi-objective fuzzy linear programming approach

Energy Technology Data Exchange (ETDEWEB)

Jana, C. [Indian Inst. of Social Welfare and Business Management, Kolkata (India); Chattopadhyay, R.N. [Indian Inst. of Technology, Kharagpur (India). Rural Development Centre

2004-09-01

Creating provisions for domestic lighting is important for rural development. Its significance in rural economy is unquestionable since some activities, like literacy, education and manufacture of craft items and other cottage products are largely dependent on domestic lighting facilities for their progress and prosperity. Thus, in rural energy planning, domestic lighting remains a key sector for allocation of investments. For rational allocation, decision makers need alternative strategies for identifying adequate and proper investment structure corresponding to appropriate sources and precise devices. The present study aims at designing a model of energy utilisation by developing a decision support frame for an optimised solution to the problem, taking into consideration four sources and six devices suitable for the study area, namely Narayangarh Block of Midnapore District in India. Since the data available from rural and unorganised sectors are often ill-defined and subjective in nature, many coefficients are fuzzy numbers, and hence several constraints appear to be fuzzy expressions. In this study, the energy allocation model is initiated with three separate objectives for optimisation, namely minimising the total cost, minimising the use of non-local sources of energy and maximising the overall efficiency of the system. Since each of the above objective-based solutions has relevance to the needs of the society and economy, it is necessary to build a model that makes a compromise among the three individual solutions. This multi-objective fuzzy linear programming (MOFLP) model, solved in a compromising decision support frame, seems to be a more rational alternative than single objective linear programming model in rural energy planning. (author)

A Solution to the Fundamental Linear Fractional Order Differential Equation

Science.gov (United States)

Hartley, Tom T.; Lorenzo, Carl F.

1998-01-01

This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.

Applied Integer Programming Modeling and Solution

CERN Document Server

Chen, Der-San; Dang, Yu

2011-01-01

An accessible treatment of the modeling and solution of integer programming problems, featuring modern applications and software In order to fully comprehend the algorithms associated with integer programming, it is important to understand not only how algorithms work, but also why they work. Applied Integer Programming features a unique emphasis on this point, focusing on problem modeling and solution using commercial software. Taking an application-oriented approach, this book addresses the art and science of mathematical modeling related to the mixed integer programming (MIP) framework and

LINEAR2007, Linear-Linear Interpolation of ENDF Format Cross-Sections

International Nuclear Information System (INIS)

2007-01-01

1 - Description of program or function: LINEAR converts evaluated cross sections in the ENDF/B format into a tabular form that is subject to linear-linear interpolation in energy and cross section. The code also thins tables of cross sections already in that form. Codes used subsequently need thus to consider only linear-linear data. IAEA1311/15: This version include the updates up to January 30, 2007. Changes in ENDF/B-VII Format and procedures, as well as the evaluations themselves, make it impossible for versions of the ENDF/B pre-processing codes earlier than PREPRO 2007 (2007 Version) to accurately process current ENDF/B-VII evaluations. The present code can handle all existing ENDF/B-VI evaluations through release 8, which will be the last release of ENDF/B-VI. Modifications from previous versions: - Linear VERS. 2007-1 (JAN. 2007): checked against all ENDF/B-VII; increased page size from 60,000 to 600,000 points 2 - Method of solution: Each section of data is considered separately. Each section of File 3, 23, and 27 data consists of a table of cross section versus energy with any of five interpolation laws. LINEAR will replace each section with a new table of energy versus cross section data in which the interpolation law is always linear in energy and cross section. The histogram (constant cross section between two energies) interpolation law is converted to linear-linear by substituting two points for each initial point. The linear-linear is not altered. For the log-linear, linear-log and log- log laws, the cross section data are converted to linear by an interval halving algorithm. Each interval is divided in half until the value at the middle of the interval can be approximated by linear-linear interpolation to within a given accuracy. The LINEAR program uses a multipoint fractional error thinning algorithm to minimize the size of each cross section table

Self-Similar Nonlinear Dynamical Solutions for One-Component Nonneutral Plasma in a Time-Dependent Linear Focusing Field

International Nuclear Information System (INIS)

Qin, Hong; Davidson, Ronald C.

2011-01-01

In a linear trap confining a one-component nonneutral plasma, the external focusing force is a linear function of the configuration coordinates and/or the velocity coordinates. Linear traps include the classical Paul trap and the Penning trap, as well as the newly proposed rotating-radio- frequency traps and the Mobius accelerator. This paper describes a class of self-similar nonlinear solutions of nonneutral plasma in general time-dependent linear focusing devices, with self-consistent electrostatic field. This class of nonlinear solutions includes many known solutions as special cases.

The PLUS family: A set of computer programs to evaluate analytical solutions of the diffusion equation and thermoelasticity

International Nuclear Information System (INIS)

Montan, D.N.

1987-02-01

This report is intended to describe, document and provide instructions for the use of new versions of a set of computer programs commonly referred to as the PLUS family. These programs were originally designed to numerically evaluate simple analytical solutions of the diffusion equation. The new versions include linear thermo-elastic effects from thermal fields calculated by the diffusion equation. After the older versions of the PLUS family were documented a year ago, it was realized that the techniques employed in the programs were well suited to the addition of linear thermo-elastic phenomena. This has been implemented and this report describes the additions. 3 refs., 14 figs

Applied Research of Enterprise Cost Control Based on Linear Programming

Directory of Open Access Journals (Sweden)

Yu Shuo

2015-01-01

This paper researches the enterprise cost control through the linear programming model, and analyzes the restriction factors of the labor of enterprise production, raw materials, processing equipment, sales price, and other factors affecting the enterprise income, so as to obtain an enterprise cost control model based on the linear programming. This model can calculate rational production mode in the case of limited resources, and acquire optimal enterprise income. The production guiding program and scheduling arrangement of the enterprise can be obtained through calculation results, so as to provide scientific and effective guidance for the enterprise production. This paper adds the sensitivity analysis in the linear programming model, so as to learn about the stability of the enterprise cost control model based on linear programming through the sensitivity analysis, and verify the rationality of the model, and indicate the direction for the enterprise cost control. The calculation results of the model can provide a certain reference for the enterprise planning in the market economy environment, which have strong reference and practical significance in terms of the enterprise cost control.

Approximate labeling via graph cuts based on linear programming.

Science.gov (United States)

Komodakis, Nikos; Tziritas, Georgios

2007-08-01

A new framework is presented for both understanding and developing graph-cut-based combinatorial algorithms suitable for the approximate optimization of a very wide class of Markov Random Fields (MRFs) that are frequently encountered in computer vision. The proposed framework utilizes tools from the duality theory of linear programming in order to provide an alternative and more general view of state-of-the-art techniques like the \\alpha-expansion algorithm, which is included merely as a special case. Moreover, contrary to \\alpha-expansion, the derived algorithms generate solutions with guaranteed optimality properties for a much wider class of problems, for example, even for MRFs with nonmetric potentials. In addition, they are capable of providing per-instance suboptimality bounds in all occasions, including discrete MRFs with an arbitrary potential function. These bounds prove to be very tight in practice (that is, very close to 1), which means that the resulting solutions are almost optimal. Our algorithms' effectiveness is demonstrated by presenting experimental results on a variety of low-level vision tasks, such as stereo matching, image restoration, image completion, and optical flow estimation, as well as on synthetic problems.

The linear stability of the Schwarzschild solution to gravitational perturbations in the generalised wave gauge

OpenAIRE

Johnson, Thomas

2018-01-01

In a recent seminal paper \\cite{D--H--R} of Dafermos, Holzegel and Rodnianski the linear stability of the Schwarzschild family of black hole solutions to the Einstein vacuum equations was established by imposing a double null gauge. In this paper we shall prove that the Schwarzschild family is linearly stable as solutions to the Einstein vacuum equations by imposing instead a generalised wave gauge: all sufficiently regular solutions to the system of equations that result from linearising the...

Joint shape segmentation with linear programming

KAUST Repository

Huang, Qixing

2011-01-01

We present an approach to segmenting shapes in a heterogenous shape database. Our approach segments the shapes jointly, utilizing features from multiple shapes to improve the segmentation of each. The approach is entirely unsupervised and is based on an integer quadratic programming formulation of the joint segmentation problem. The program optimizes over possible segmentations of individual shapes as well as over possible correspondences between segments from multiple shapes. The integer quadratic program is solved via a linear programming relaxation, using a block coordinate descent procedure that makes the optimization feasible for large databases. We evaluate the presented approach on the Princeton segmentation benchmark and show that joint shape segmentation significantly outperforms single-shape segmentation techniques. © 2011 ACM.

Classical solutions of non-linear sigma-models and their quantum fluctuations

International Nuclear Information System (INIS)

Din, A.M.

1980-05-01

I study the properties of O(N) and CPsup(n-1) non-linear sigma-models in the two dimensional Euclidean space. All classical solutions of the equations of motion can be characterized and in the CPsup(n-1) model they can be expressed in a simple and explicit way in terms of holomorphic vectors. The topological winding number and the action of the general CPsup(n-1) solution can be evaluated and the latter turns out always to be a integer multiple of 2π. I further discuss the stability of the solutions and the problem of one-loop calculations of quantum fluctuations around classical solutions

Radial solutions to semilinear elliptic equations via linearized operators

Directory of Open Access Journals (Sweden)

Phuong Le

2017-04-01

Full Text Available Let $u$ be a classical solution of semilinear elliptic equations in a ball or an annulus in $\\mathbb{R}^N$ with zero Dirichlet boundary condition where the nonlinearity has a convex first derivative. In this note, we prove that if the $N$-th eigenvalue of the linearized operator at $u$ is positive, then $u$ must be radially symmetric.

Phantom solution in a non-linear Israel-Stewart theory

Science.gov (United States)

Cruz, Miguel; Cruz, Norman; Lepe, Samuel

2017-06-01

In this paper we present a phantom solution with a big rip singularity in a non-linear regime of the Israel-Stewart formalism. In this framework it is possible to extend this causal formalism in order to describe accelerated expansion, where assumption of near equilibrium is no longer valid. We assume a flat universe filled with a single viscous fluid ruled by a barotropic EoS, p = ωρ, which can represent a late time accelerated phase of the cosmic evolution. The solution allows to cross the phantom divide without evoking an exotic matter fluid and the effective EoS parameter is always lesser than -1 and constant in time.

Arc-Search Infeasible Interior-Point Algorithm for Linear Programming

OpenAIRE

Yang, Yaguang

2014-01-01

Mehrotra's algorithm has been the most successful infeasible interior-point algorithm for linear programming since 1990. Most popular interior-point software packages for linear programming are based on Mehrotra's algorithm. This paper proposes an alternative algorithm, arc-search infeasible interior-point algorithm. We will demonstrate, by testing Netlib problems and comparing the test results obtained by arc-search infeasible interior-point algorithm and Mehrotra's algorithm, that the propo...

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.

Object matching using a locally affine invariant and linear programming techniques.

Science.gov (United States)

Li, Hongsheng; Huang, Xiaolei; He, Lei

2013-02-01

In this paper, we introduce a new matching method based on a novel locally affine-invariant geometric constraint and linear programming techniques. To model and solve the matching problem in a linear programming formulation, all geometric constraints should be able to be exactly or approximately reformulated into a linear form. This is a major difficulty for this kind of matching algorithm. We propose a novel locally affine-invariant constraint which can be exactly linearized and requires a lot fewer auxiliary variables than other linear programming-based methods do. The key idea behind it is that each point in the template point set can be exactly represented by an affine combination of its neighboring points, whose weights can be solved easily by least squares. Errors of reconstructing each matched point using such weights are used to penalize the disagreement of geometric relationships between the template points and the matched points. The resulting overall objective function can be solved efficiently by linear programming techniques. Our experimental results on both rigid and nonrigid object matching show the effectiveness of the proposed algorithm.

A Test of a Linear Programming Model as an Optimal Solution to the Problem of Combining Methods of Reading Instruction

Science.gov (United States)

Mills, James W.; And Others

1973-01-01

The Study reported here tested an application of the Linear Programming Model at the Reading Clinic of Drew University. Results, while not conclusive, indicate that this approach yields greater gains in speed scores than a traditional approach for this population. (Author)

Improved pedagogy for linear differential equations by reconsidering how we measure the size of solutions

Science.gov (United States)

Tisdell, Christopher C.

2017-11-01

For over 50 years, the learning of teaching of a priori bounds on solutions to linear differential equations has involved a Euclidean approach to measuring the size of a solution. While the Euclidean approach to a priori bounds on solutions is somewhat manageable in the learning and teaching of the proofs involving second-order, linear problems with constant co-efficients, we believe it is not pedagogically optimal. Moreover, the Euclidean method becomes pedagogically unwieldy in the proofs involving higher-order cases. The purpose of this work is to propose a simpler pedagogical approach to establish a priori bounds on solutions by considering a different way of measuring the size of a solution to linear problems, which we refer to as the Uber size. The Uber form enables a simplification of pedagogy from the literature and the ideas are accessible to learners who have an understanding of the Fundamental Theorem of Calculus and the exponential function, both usually seen in a first course in calculus. We believe that this work will be of mathematical and pedagogical interest to those who are learning and teaching in the area of differential equations or in any of the numerous disciplines where linear differential equations are used.

Application of integer programming on logistics solution for load transportation: the solver tool and its limitations in the search for the optimal solution

Directory of Open Access Journals (Sweden)

Ricardo França Santos

2012-01-01

Full Text Available This work tries to solve a typical logistics problem of Navy of Brazil regards the allocation, transportation and distribution of genera refrigerated for Military Organizations within Grande Rio (RJ. After a brief review of literature on Linear/Integer Programming and some of their applications, we proposed the use of Integer Programming, using the Excel’s Solver as a tool for obtaining the optimal load configuration for the fleet, obtaining the lower distribution costs in order to meet the demand schedule. The assumptions were met in a first attempt with a single spreadsheet, but it could not find a convergent solution, without degeneration problems and with a reasonable solution time. A second solution was proposed separating the problem into three phases, which allowed us to highlight the potential and limitations of the Solver tool. This study showed the importance of formulating a realistic model and of a detailed critical analysis, which could be seen through the lack of convergence of the first solution and the success achieved by the second one.

Linear and quadratic exponential modulation of the solutions of the paraxial wave equation

International Nuclear Information System (INIS)

Torre, A

2010-01-01

A review of well-known transformations, which allow us to pass from one solution of the paraxial wave equation (PWE) (in one transverse space variable) to another, is presented. Such transformations are framed within the unifying context of the Lie algebra formalism, being related indeed to symmetries of the PWE. Due to the closure property of the symmetry group of the PWE we are led to consider as not trivial only the linear and the quadratic exponential modulation (accordingly, accompanied by a suitable shift or scaling of the space variables) of the original solutions of the PWE, which are seen to be just conveyed by a linear and a quadratic exponential modulation of the relevant 'source' functions. We will see that recently introduced solutions of the 1D PWE in both rectangular and polar coordinates can be deduced from already known solutions through the resulting symmetry transformation related schemes

Sequential computation of elementary modes and minimal cut sets in genome-scale metabolic networks using alternate integer linear programming

Energy Technology Data Exchange (ETDEWEB)

Song, Hyun-Seob; Goldberg, Noam; Mahajan, Ashutosh; Ramkrishna, Doraiswami

2017-03-27

Elementary (flux) modes (EMs) have served as a valuable tool for investigating structural and functional properties of metabolic networks. Identification of the full set of EMs in genome-scale networks remains challenging due to combinatorial explosion of EMs in complex networks. It is often, however, that only a small subset of relevant EMs needs to be known, for which optimization-based sequential computation is a useful alternative. Most of the currently available methods along this line are based on the iterative use of mixed integer linear programming (MILP), the effectiveness of which significantly deteriorates as the number of iterations builds up. To alleviate the computational burden associated with the MILP implementation, we here present a novel optimization algorithm termed alternate integer linear programming (AILP). Results: Our algorithm was designed to iteratively solve a pair of integer programming (IP) and linear programming (LP) to compute EMs in a sequential manner. In each step, the IP identifies a minimal subset of reactions, the deletion of which disables all previously identified EMs. Thus, a subsequent LP solution subject to this reaction deletion constraint becomes a distinct EM. In cases where no feasible LP solution is available, IP-derived reaction deletion sets represent minimal cut sets (MCSs). Despite the additional computation of MCSs, AILP achieved significant time reduction in computing EMs by orders of magnitude. The proposed AILP algorithm not only offers a computational advantage in the EM analysis of genome-scale networks, but also improves the understanding of the linkage between EMs and MCSs.

Asymptotical Behavior of the Solution of a SDOF Linear Fractionally Damped Vibration System

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Z.H. Wang

2011-01-01

Full Text Available Fractional-order derivative has been shown an adequate tool to the study of so-called "anomalous" social and physical behaviors, in reflecting their non-local, frequency- and history-dependent properties, and it has been used to model practical systems in engineering successfully, including the famous Bagley-Torvik equation modeling forced motion of a rigid plate immersed in Newtonian fluid. The solutions of the initial value problems of linear fractional differential equations are usually expressed in terms of Mittag-Leffler functions or some other kind of power series. Such forms of solutions are not good for engineers not only in understanding the solutions but also in investigation. This paper proves that for the linear SDOF oscillator with a damping described by fractional-order derivative whose order is between 1 and 2, the solution of its initial value problem free of external excitation consists of two parts, the first one is the 'eigenfunction expansion' that is similar to the case without fractional-order derivative, and the second one is a definite integral that is independent of the eigenvalues (or characteristic roots. The integral disappears in the classical linear oscillator and it can be neglected from the solution when stationary solution is addressed. Moreover, the response of the fractionally damped oscillator under harmonic excitation is calculated in a similar way, and it is found that the fractional damping with order between 1 and 2 can be used to produce oscillation with large amplitude as well as to suppress oscillation, depending on the ratio of the excitation frequency and the natural frequency.

Application of the simplex method of linear programming model to ...

African Journals Online (AJOL)

This work discussed how the simplex method of linear programming could be used to maximize the profit of any business firm using Saclux Paint Company as a case study. It equally elucidated the effect variation in the optimal result obtained from linear programming model, will have on any given firm. It was demonstrated ...

Finite element historical deformation analysis in piecewise linear plasticity by mathematical programming

International Nuclear Information System (INIS)

De Donato, O.; Parisi, M.A.

1977-01-01

When loads increase proportionally beyond the elastic limit in the presence of elastic-plastic piecewise-linear constitutive laws, the problem of finding the whole evolution of the plastic strain and displacements of structures was recently shown to be amenable to a parametric linear complementary problem (PLCP) in which the parameter is represented by the load factor, the matrix is symmetric positive definite or at least semi-definite (for perfect plasticity) and the variables with a direct mechanical meaning are the plastic multipliers. With reference to plane trusses and frames with elastic-plastic linear work-hardening material behaviour numerical solutions were also fairly efficiently obtained using a recent mathematical programming algorithm (due to R.W. Cottle) which is able to provide the whole deformation history of the structure and, at the same time to rule out local unloadings along the given proportional loading process by means of 'a priori' checks carried out before each pivotal step of the procedure. Hence it becomes possible to use the holonomic (reversible, path-independent) constitutive laws in finite terms and to benefit by all the relevant numerical and computational advantages despite the non-holonomic nature of plastic behaviour. In the present paper the method of solution is re-examined in view to overcome an important drawback of the algorithm deriving from the size of PLCP fully populated matrix when structural problems with large number of variables are considered and, consequently, the updating, the storing or, generally, the handling of the current tableau may become prohibitive. (Auth.)

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

A note on the time decay of solutions for the linearized Wigner-Poisson system

KAUST Repository

Gamba, Irene; Gualdani, Maria; Sparber, Christof

2009-01-01

We consider the one-dimensional Wigner-Poisson system of plasma physics, linearized around a (spatially homogeneous) Lorentzian distribution and prove that the solution of the corresponding linearized problem decays to zero in time. We also give

On the economical solution method for a system of linear algebraic equations

Directory of Open Access Journals (Sweden)

Jan Awrejcewicz

2004-01-01

Full Text Available The present work proposes a novel optimal and exact method of solving large systems of linear algebraic equations. In the approach under consideration, the solution of a system of algebraic linear equations is found as a point of intersection of hyperplanes, which needs a minimal amount of computer operating storage. Two examples are given. In the first example, the boundary value problem for a three-dimensional stationary heat transfer equation in a parallelepiped in ℝ3 is considered, where boundary value problems of first, second, or third order, or their combinations, are taken into account. The governing differential equations are reduced to algebraic ones with the help of the finite element and boundary element methods for different meshes applied. The obtained results are compared with known analytical solutions. The second example concerns computation of a nonhomogeneous shallow physically and geometrically nonlinear shell subject to transversal uniformly distributed load. The partial differential equations are reduced to a system of nonlinear algebraic equations with the error of O(hx12+hx22. The linearization process is realized through either Newton method or differentiation with respect to a parameter. In consequence, the relations of the boundary condition variations along the shell side and the conditions for the solution matching are reported.

An Optimal Linear Coding for Index Coding Problem

OpenAIRE

Pezeshkpour, Pouya

2015-01-01

An optimal linear coding solution for index coding problem is established. Instead of network coding approach by focus on graph theoric and algebraic methods a linear coding program for solving both unicast and groupcast index coding problem is presented. The coding is proved to be the optimal solution from the linear perspective and can be easily utilize for any number of messages. The importance of this work is lying mostly on the usage of the presented coding in the groupcast index coding ...

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.

Stability of the trivial solution for linear stochastic differential equations with Poisson white noise

International Nuclear Information System (INIS)

Grigoriu, Mircea; Samorodnitsky, Gennady

2004-01-01

Two methods are considered for assessing the asymptotic stability of the trivial solution of linear stochastic differential equations driven by Poisson white noise, interpreted as the formal derivative of a compound Poisson process. The first method attempts to extend a result for diffusion processes satisfying linear stochastic differential equations to the case of linear equations with Poisson white noise. The developments for the method are based on Ito's formula for semimartingales and Lyapunov exponents. The second method is based on a geometric ergodic theorem for Markov chains providing a criterion for the asymptotic stability of the solution of linear stochastic differential equations with Poisson white noise. Two examples are presented to illustrate the use and evaluate the potential of the two methods. The examples demonstrate limitations of the first method and the generality of the second method

A Direct Heuristic Algorithm for Linear Programming

Indian Academy of Sciences (India)

Abstract. An (3) mathematically non-iterative heuristic procedure that needs no artificial variable is presented for solving linear programming problems. An optimality test is included. Numerical experiments depict the utility/scope of such a procedure.

Train Repathing in Emergencies Based on Fuzzy Linear Programming

Directory of Open Access Journals (Sweden)

Xuelei Meng

2014-01-01

Full Text Available Train pathing is a typical problem which is to assign the train trips on the sets of rail segments, such as rail tracks and links. This paper focuses on the train pathing problem, determining the paths of the train trips in emergencies. We analyze the influencing factors of train pathing, such as transferring cost, running cost, and social adverse effect cost. With the overall consideration of the segment and station capability constraints, we build the fuzzy linear programming model to solve the train pathing problem. We design the fuzzy membership function to describe the fuzzy coefficients. Furthermore, the contraction-expansion factors are introduced to contract or expand the value ranges of the fuzzy coefficients, coping with the uncertainty of the value range of the fuzzy coefficients. We propose a method based on triangular fuzzy coefficient and transfer the train pathing (fuzzy linear programming model to a determinate linear model to solve the fuzzy linear programming problem. An emergency is supposed based on the real data of the Beijing-Shanghai Railway. The model in this paper was solved and the computation results prove the availability of the model and efficiency of the algorithm.

Train repathing in emergencies based on fuzzy linear programming.

Science.gov (United States)

Meng, Xuelei; Cui, Bingmou

2014-01-01

Train pathing is a typical problem which is to assign the train trips on the sets of rail segments, such as rail tracks and links. This paper focuses on the train pathing problem, determining the paths of the train trips in emergencies. We analyze the influencing factors of train pathing, such as transferring cost, running cost, and social adverse effect cost. With the overall consideration of the segment and station capability constraints, we build the fuzzy linear programming model to solve the train pathing problem. We design the fuzzy membership function to describe the fuzzy coefficients. Furthermore, the contraction-expansion factors are introduced to contract or expand the value ranges of the fuzzy coefficients, coping with the uncertainty of the value range of the fuzzy coefficients. We propose a method based on triangular fuzzy coefficient and transfer the train pathing (fuzzy linear programming model) to a determinate linear model to solve the fuzzy linear programming problem. An emergency is supposed based on the real data of the Beijing-Shanghai Railway. The model in this paper was solved and the computation results prove the availability of the model and efficiency of the algorithm.

Study and program implementation of transient curves' piecewise linearization

International Nuclear Information System (INIS)

Shi Yang; Zu Hongbiao

2014-01-01

Background: Transient curves are essential for the stress analysis of related equipment in nuclear power plant (NPP). The actually operating data or the design transient data of a NPP usually consist of a large number of data points with very short time intervals. To simplify the analysis, transient curves are generally piecewise linearized in advance. Up to now, the piecewise linearization of transient curves is accomplished manually, Purpose: The aim is to develop a method for the piecewise linearization of transient curves, and to implement it by programming. Methods: First of all, the fitting line of a number of data points was obtained by the least square method. The segment of the fitting line is set while the accumulation error of linearization exceeds the preset limit with the increasing number of points. Then the linearization of subsequent data points was begun from the last point of the preceding curve segment to get the next segment in the same way, and continue until the final data point involved. Finally, averaging of junction points is taken for the segment connection. Results: A computer program named PLTC (Piecewise Linearization for Transient Curves) was implemented and verified by the linearization of the standard sine curve and typical transient curves of a NPP. Conclusion: The method and the PLTC program can be well used to the piecewise linearization of transient curves, with improving efficiency and precision. (authors)

Linear Programming for Vocational Education Planning. Interim Report.

Science.gov (United States)

Young, Robert C.; And Others

The purpose of the paper is to define for potential users of vocational education management information systems a quantitative analysis technique and its utilization to facilitate more effective planning of vocational education programs. Defining linear programming (LP) as a management technique used to solve complex resource allocation problems…

A note on the time decay of solutions for the linearized Wigner-Poisson system

KAUST Repository

Gamba, Irene

2009-01-01

We consider the one-dimensional Wigner-Poisson system of plasma physics, linearized around a (spatially homogeneous) Lorentzian distribution and prove that the solution of the corresponding linearized problem decays to zero in time. We also give an explicit algebraic decay rate.

The Computer Program LIAR for Beam Dynamics Calculations in Linear Accelerators

International Nuclear Information System (INIS)

Assmann, R.W.; Adolphsen, C.; Bane, K.; Raubenheimer, T.O.; Siemann, R.H.; Thompson, K.

2011-01-01

Linear accelerators are the central components of the proposed next generation of linear colliders. They need to provide acceleration of up to 750 GeV per beam while maintaining very small normalized emittances. Standard simulation programs, mainly developed for storage rings, do not meet the specific requirements for high energy linear accelerators. We present a new program LIAR ('LInear Accelerator Research code') that includes wakefield effects, a 6D coupled beam description, specific optimization algorithms and other advanced features. Its modular structure allows to use and to extend it easily for different purposes. The program is available for UNIX workstations and Windows PC's. It can be applied to a broad range of accelerators. We present examples of simulations for SLC and NLC.

The Use of Linear Programming for Prediction.

Science.gov (United States)

Schnittjer, Carl J.

The purpose of the study was to develop a linear programming model to be used for prediction, test the accuracy of the predictions, and compare the accuracy with that produced by curvilinear multiple regression analysis. (Author)

The RANDOM computer program: A linear congruential random number generator

Science.gov (United States)

Miles, R. F., Jr.

1986-01-01

The RANDOM Computer Program is a FORTRAN program for generating random number sequences and testing linear congruential random number generators (LCGs). The linear congruential form of random number generator is discussed, and the selection of parameters of an LCG for a microcomputer described. This document describes the following: (1) The RANDOM Computer Program; (2) RANDOM.MOD, the computer code needed to implement an LCG in a FORTRAN program; and (3) The RANCYCLE and the ARITH Computer Programs that provide computational assistance in the selection of parameters for an LCG. The RANDOM, RANCYCLE, and ARITH Computer Programs are written in Microsoft FORTRAN for the IBM PC microcomputer and its compatibles. With only minor modifications, the RANDOM Computer Program and its LCG can be run on most micromputers or mainframe computers.

Using linear programming to analyze and optimize stochastic flow lines

DEFF Research Database (Denmark)

Helber, Stefan; Schimmelpfeng, Katja; Stolletz, Raik

2011-01-01

This paper presents a linear programming approach to analyze and optimize flow lines with limited buffer capacities and stochastic processing times. The basic idea is to solve a huge but simple linear program that models an entire simulation run of a multi-stage production process in discrete time...... programming and hence allows us to solve buffer allocation problems. We show under which conditions our method works well by comparing its results to exact values for two-machine models and approximate simulation results for longer lines....

Oscillation and nonoscillation results for solutions of half-linear equations with deviated argument

Czech Academy of Sciences Publication Activity Database

Drábek, P.; Kufner, Alois; Kuliev, K.

2017-01-01

Roč. 447, č. 1 (2017), s. 371-382 ISSN 0022-247X Institutional support: RVO:67985840 Keywords : half-linear equation * oscillatory solution * nonoscillatory solution Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.064, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022247X16306059

A general method for enclosing solutions of interval linear equations

Czech Academy of Sciences Publication Activity Database

Rohn, Jiří

2012-01-01

Roč. 6, č. 4 (2012), s. 709-717 ISSN 1862-4472 R&D Projects: GA ČR GA201/09/1957; GA ČR GC201/08/J020 Institutional research plan: CEZ:AV0Z10300504 Keywords : interval linear equations * solution set * enclosure * absolute value inequality Subject RIV: BA - General Mathematics Impact factor: 1.654, year: 2012

Approximating the Pareto Set of Multiobjective Linear Programs via Robust Optimization

NARCIS (Netherlands)

Gorissen, B.L.; den Hertog, D.

2012-01-01

Abstract: The Pareto set of a multiobjective optimization problem consists of the solutions for which one or more objectives can not be improved without deteriorating one or more other objectives. We consider problems with linear objectives and linear constraints and use Adjustable Robust

Linear Scaling Solution of the Time-Dependent Self-Consistent-Field Equations

Directory of Open Access Journals (Sweden)

Matt Challacombe

2014-03-01

Full Text Available A new approach to solving the Time-Dependent Self-Consistent-Field equations is developed based on the double quotient formulation of Tsiper 2001 (J. Phys. B. Dual channel, quasi-independent non-linear optimization of these quotients is found to yield convergence rates approaching those of the best case (single channel Tamm-Dancoff approximation. This formulation is variational with respect to matrix truncation, admitting linear scaling solution of the matrix-eigenvalue problem, which is demonstrated for bulk excitons in the polyphenylene vinylene oligomer and the (4,3 carbon nanotube segment.

Near-Regular Structure Discovery Using Linear Programming

KAUST Repository

Huang, Qixing; Guibas, Leonidas J.; Mitra, Niloy J.

2014-01-01

as an optimization and efficiently solve it using linear programming techniques. Our optimization has a discrete aspect, that is, the connectivity relationships among the elements, as well as a continuous aspect, namely the locations of the elements of interest. Both

NP-Hardness of optimizing the sum of Rational Linear Functions over an Asymptotic-Linear-Program

OpenAIRE

Chermakani, Deepak Ponvel

2012-01-01

We convert, within polynomial-time and sequential processing, an NP-Complete Problem into a real-variable problem of minimizing a sum of Rational Linear Functions constrained by an Asymptotic-Linear-Program. The coefficients and constants in the real-variable problem are 0, 1, -1, K, or -K, where K is the time parameter that tends to positive infinity. The number of variables, constraints, and rational linear functions in the objective, of the real-variable problem is bounded by a polynomial ...

Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs

NARCIS (Netherlands)

R.A. Zuidwijk (Rob)

2005-01-01

textabstractSensitivity analysis is used to quantify the impact of changes in the initial data of linear programs on the optimal value. In particular, parametric sensitivity analysis involves a perturbation analysis in which the effects of small changes of some or all of the initial data on an

Synthesizing Dynamic Programming Algorithms from Linear Temporal Logic Formulae

Science.gov (United States)

Rosu, Grigore; Havelund, Klaus

2001-01-01

The problem of testing a linear temporal logic (LTL) formula on a finite execution trace of events, generated by an executing program, occurs naturally in runtime analysis of software. We present an algorithm which takes an LTL formula and generates an efficient dynamic programming algorithm. The generated algorithm tests whether the LTL formula is satisfied by a finite trace of events given as input. The generated algorithm runs in linear time, its constant depending on the size of the LTL formula. The memory needed is constant, also depending on the size of the formula.

Asymptotic behavior of solutions of linear multi-order fractional differential equation systems

OpenAIRE

Diethelm, Kai; Siegmund, Stefan; Tuan, H. T.

2017-01-01

In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential equation systems. Next, a representation of solutions of homogeneous linear multi-order fractional differential equation systems in series form is provided. Finally, we give characteristics regarding the asymptotic behavior of solutions to some classes of line...

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

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

Description of All Solutions of a Linear Complementarity Problem

Czech Academy of Sciences Publication Activity Database

Rohn, Jiří

2009-01-01

Roč. 18, - (2009), s. 246-252 E-ISSN 1081-3810 R&D Projects: GA ČR GA201/09/1957; GA ČR GC201/08/J020 Institutional research plan: CEZ:AV0Z10300504 Keywords : linear complementarity problem * Moore-Penrose inverse * verified solution * absolute value equation Subject RIV: BA - General Mathematics Impact factor: 0.892, year: 2009 http://www.math.technion.ac.il/iic/ ela / ela -articles/articles/vol18_pp246-252.pdf

Program LINEAR (version 79-1): linearize data in the evaluated nuclear data file/version B (ENDF/B) format

International Nuclear Information System (INIS)

Cullen, D.E.

1979-01-01

Program LINEAR converts evaluated cross sections in the ENDF/B format into a tabular form that is subject to linear-linear interpolation in energy and cross section. The code also thins tables of cross sections already in that form (i.e., removes points not needed for linear interpolability). The main advantage of the code is that it allows subsequent codes to consider only linear-linear data. A listing of the source deck is available on request

On the multisummability of WKB solutions of certain singularly perturbed linear ordinary differential equations

Directory of Open Access Journals (Sweden)

Yoshitsugu Takei

2015-01-01

Full Text Available Using two concrete examples, we discuss the multisummability of WKB solutions of singularly perturbed linear ordinary differential equations. Integral representations of solutions and a criterion for the multisummability based on the Cauchy-Heine transform play an important role in the proof.

A linear programming approach for placement of applicants to academic programs

OpenAIRE

Kassa, Biniyam Asmare

2013-01-01

This paper reports a linear programming approach for placement of applicants to study programs developed and implemented at the college of Business & Economics, Bahir Dar University, Bahir Dar, Ethiopia. The approach is estimated to significantly streamline the placement decision process at the college by reducing required man hour as well as the time it takes to announce placement decisions. Compared to the previous manual system where only one or two placement criteria were considered, the ...

Solution of linear ordinary differential equations by means of the method of variation of arbitrary constants

DEFF Research Database (Denmark)

Mejlbro, Leif

1997-01-01

An alternative formula for the solution of linear differential equations of order n is suggested. When applicable, the suggested method requires fewer and simpler computations than the well-known method using Wronskians.......An alternative formula for the solution of linear differential equations of order n is suggested. When applicable, the suggested method requires fewer and simpler computations than the well-known method using Wronskians....

Numerical linear algebra theory and applications

CERN Document Server

Beilina, Larisa; Karchevskii, Mikhail

2017-01-01

This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigen problems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.

"Real-Time Optical Laboratory Linear Algebra Solution Of Partial Differential Equations"

Science.gov (United States)

Casasent, David; Jackson, James

1986-03-01

A Space Integrating (SI) Optical Linear Algebra Processor (OLAP) employing space and frequency-multiplexing, new partitioning and data flow, and achieving high accuracy performance with a non base-2 number system is described. Laboratory data on the performance of this system and the solution of parabolic Partial Differential Equations (PDEs) is provided. A multi-processor OLAP system is also described for the first time. It use in the solution of multiple banded matrices that frequently arise is then discussed. The utility and flexibility of this processor compared to digital systolic architectures should be apparent.

Statistical mechanical analysis of linear programming relaxation for combinatorial optimization problems

Science.gov (United States)

Takabe, Satoshi; Hukushima, Koji

2016-05-01

Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α -uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α =2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c =e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c =1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α ≥3 , minimum vertex covers on α -uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c =e /(α -1 ) where the replica symmetry is broken.

Statistical mechanical analysis of linear programming relaxation for combinatorial optimization problems.

Science.gov (United States)

Takabe, Satoshi; Hukushima, Koji

2016-05-01

Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α-uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α=2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c=e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c=1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α≥3, minimum vertex covers on α-uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c=e/(α-1) where the replica symmetry is broken.

Updating QR factorization procedure for solution of linear least squares problem with equality constraints.

Science.gov (United States)

Zeb, Salman; Yousaf, Muhammad

2017-01-01

In this article, we present a QR updating procedure as a solution approach for linear least squares problem with equality constraints. We reduce the constrained problem to unconstrained linear least squares and partition it into a small subproblem. The QR factorization of the subproblem is calculated and then we apply updating techniques to its upper triangular factor R to obtain its solution. We carry out the error analysis of the proposed algorithm to show that it is backward stable. We also illustrate the implementation and accuracy of the proposed algorithm by providing some numerical experiments with particular emphasis on dense problems.

Solutions of First-Order Volterra Type Linear Integrodifferential Equations by Collocation Method

Directory of Open Access Journals (Sweden)

Olumuyiwa A. Agbolade

2017-01-01

Full Text Available The numerical solutions of linear integrodifferential equations of Volterra type have been considered. Power series is used as the basis polynomial to approximate the solution of the problem. Furthermore, standard and Chebyshev-Gauss-Lobatto collocation points were, respectively, chosen to collocate the approximate solution. Numerical experiments are performed on some sample problems already solved by homotopy analysis method and finite difference methods. Comparison of the absolute error is obtained from the present method and those from aforementioned methods. It is also observed that the absolute errors obtained are very low establishing convergence and computational efficiency.

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

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.

Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation

International Nuclear Information System (INIS)

Kolesov, Andrei Yu; Rozov, Nikolai Kh

2002-01-01

For the non-linear telegraph equation with homogeneous Dirichlet or Neumann conditions at the end-points of a finite interval the question of the existence and the stability of time-periodic solutions bifurcating from the zero equilibrium state is considered. The dynamics of these solutions under a change of the diffusion coefficient (that is, the coefficient of the second derivative with respect to the space variable) is investigated. For the Dirichlet boundary conditions it is shown that this dynamics substantially depends on the presence - or the absence - of quadratic terms in the non-linearity. More precisely, it is shown that a quadratic non-linearity results in the occurrence, under an unbounded decrease of diffusion, of an infinite sequence of bifurcations of each periodic solution. En route, the related issue of the limits of applicability of Yu.S. Kolesov's method of quasinormal forms to the construction of self-oscillations in singularly perturbed hyperbolic boundary value problems is studied

Systems analysis on the condition of market penetration for hydrogen technologies using linear programming model

International Nuclear Information System (INIS)

Kato, K.; Ihara, S.

1993-01-01

Hydrogen is expected to be an important energy carrier, especially in the frame of global warming problem solution. The purpose of this study is to examine the condition of market penetration of hydrogen technologies in reducing CO 2 emissions. A multi-time-period linear programming model (MARKAL, Market Allocation)) is used to explore technology options and cost for meeting the energy demands while reducing CO 2 emissions from energy systems. The results show that hydrogen technologies become economical when CO 2 emissions are stringently constrained. 9 figs., 2 refs

Sequential computation of elementary modes and minimal cut sets in genome-scale metabolic networks using alternate integer linear programming.

Science.gov (United States)

Song, Hyun-Seob; Goldberg, Noam; Mahajan, Ashutosh; Ramkrishna, Doraiswami

2017-08-01

Elementary (flux) modes (EMs) have served as a valuable tool for investigating structural and functional properties of metabolic networks. Identification of the full set of EMs in genome-scale networks remains challenging due to combinatorial explosion of EMs in complex networks. It is often, however, that only a small subset of relevant EMs needs to be known, for which optimization-based sequential computation is a useful alternative. Most of the currently available methods along this line are based on the iterative use of mixed integer linear programming (MILP), the effectiveness of which significantly deteriorates as the number of iterations builds up. To alleviate the computational burden associated with the MILP implementation, we here present a novel optimization algorithm termed alternate integer linear programming (AILP). Our algorithm was designed to iteratively solve a pair of integer programming (IP) and linear programming (LP) to compute EMs in a sequential manner. In each step, the IP identifies a minimal subset of reactions, the deletion of which disables all previously identified EMs. Thus, a subsequent LP solution subject to this reaction deletion constraint becomes a distinct EM. In cases where no feasible LP solution is available, IP-derived reaction deletion sets represent minimal cut sets (MCSs). Despite the additional computation of MCSs, AILP achieved significant time reduction in computing EMs by orders of magnitude. The proposed AILP algorithm not only offers a computational advantage in the EM analysis of genome-scale networks, but also improves the understanding of the linkage between EMs and MCSs. The software is implemented in Matlab, and is provided as supplementary information . hyunseob.song@pnnl.gov. Supplementary data are available at Bioinformatics online. Published by Oxford University Press 2017. This work is written by US Government employees and are in the public domain in the US.

Improved Pedagogy for Linear Differential Equations by Reconsidering How We Measure the Size of Solutions

Science.gov (United States)

Tisdell, Christopher C.

2017-01-01

For over 50 years, the learning of teaching of "a priori" bounds on solutions to linear differential equations has involved a Euclidean approach to measuring the size of a solution. While the Euclidean approach to "a priori" bounds on solutions is somewhat manageable in the learning and teaching of the proofs involving…

Multiobjective Optimization of Linear Cooperative Spectrum Sensing: Pareto Solutions and Refinement.

Science.gov (United States)

Yuan, Wei; You, Xinge; Xu, Jing; Leung, Henry; Zhang, Tianhang; Chen, Chun Lung Philip

2016-01-01

In linear cooperative spectrum sensing, the weights of secondary users and detection threshold should be optimally chosen to minimize missed detection probability and to maximize secondary network throughput. Since these two objectives are not completely compatible, we study this problem from the viewpoint of multiple-objective optimization. We aim to obtain a set of evenly distributed Pareto solutions. To this end, here, we introduce the normal constraint (NC) method to transform the problem into a set of single-objective optimization (SOO) problems. Each SOO problem usually results in a Pareto solution. However, NC does not provide any solution method to these SOO problems, nor any indication on the optimal number of Pareto solutions. Furthermore, NC has no preference over all Pareto solutions, while a designer may be only interested in some of them. In this paper, we employ a stochastic global optimization algorithm to solve the SOO problems, and then propose a simple method to determine the optimal number of Pareto solutions under a computational complexity constraint. In addition, we extend NC to refine the Pareto solutions and select the ones of interest. Finally, we verify the effectiveness and efficiency of the proposed methods through computer simulations.

Chromosome structures: reduction of certain problems with unequal gene content and gene paralogs to integer linear programming.

Science.gov (United States)

Lyubetsky, Vassily; Gershgorin, Roman; Gorbunov, Konstantin

2017-12-06

problems can be reduced to integer linear programming formulations, which allows an algorithm to redefine the problems to implement a very special case of the integer linear programming tool. The results were tested on synthetic and biological samples. Three well-known problems were reduced to a very special case of integer linear programming, which is a new method of their solutions. Integer linear programming is clearly among the main computational methods and, as generally accepted, is fast on average; in particular, computation systems specifically targeted at it are available. The challenges are to reduce the size of the corresponding integer linear programming formulations and to incorporate a more detailed biological concept in our model of the reconstruction.

Generalised Assignment Matrix Methodology in Linear Programming

Science.gov (United States)

Jerome, Lawrence

2012-01-01

Discrete Mathematics instructors and students have long been struggling with various labelling and scanning algorithms for solving many important problems. This paper shows how to solve a wide variety of Discrete Mathematics and OR problems using assignment matrices and linear programming, specifically using Excel Solvers although the same…

Solving a mixed-integer linear programming model for a multi-skilled project scheduling problem by simulated annealing

Directory of Open Access Journals (Sweden)

H Kazemipoor

2012-04-01

Full Text Available A multi-skilled project scheduling problem (MSPSP has been generally presented to schedule a project with staff members as resources. Each activity in project network requires different skills and also staff members have different skills, too. This causes the MSPSP becomes a special type of a multi-mode resource-constrained project scheduling problem (MM-RCPSP with a huge number of modes. Given the importance of this issue, in this paper, a mixed integer linear programming for the MSPSP is presented. Due to the complexity of the problem, a meta-heuristic algorithm is proposed in order to find near optimal solutions. To validate performance of the algorithm, results are compared against exact solutions solved by the LINGO solver. The results are promising and show that optimal or near-optimal solutions are derived for small instances and good solutions for larger instances in reasonable time.

The Solution Set Characterization and Error Bound for the Extended Mixed Linear Complementarity Problem

Directory of Open Access Journals (Sweden)

Hongchun Sun

2012-01-01

Full Text Available For the extended mixed linear complementarity problem (EML CP, we first present the characterization of the solution set for the EMLCP. Based on this, its global error bound is also established under milder conditions. The results obtained in this paper can be taken as an extension for the classical linear complementarity problems.

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.

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.

Parallelized preconditioned BiCGStab solution of sparse linear system equations in F-COBRA-TF

International Nuclear Information System (INIS)

Geemert, Rene van; Glück, Markus; Riedmann, Michael; Gabriel, Harry

2011-01-01

Recently, the in-house development of a preconditioned and parallelized BiCGStab solver has been pursued successfully in AREVA’s advanced sub-channel code F-COBRA-TF. This solver can be run either in a sequential computation mode on a single CPU, or in a parallel computation mode on multiple parallel CPUs. The developed procedure enables the computation of several thousands of successive sparse linear system solutions in F-COBRA-TF with acceptable wall clock run times. The current paper provides general information about F-COBRA-TF in terms of modeling capabilities and application areas, and points out where the relevance arises for the efficient iterative solution of sparse linear systems. Furthermore, the preconditioning and parallelization strategies in the developed BiCGStab iterative solution approach are discussed. The paper is concluded with a number of verification examples. (author)

Solutions of half-linear differential equations in the classes Gamma and Pi

Czech Academy of Sciences Publication Activity Database

Řehák, Pavel; Taddei, V.

2016-01-01

Roč. 29, 7-8 (2016), s. 683-714 ISSN 0893-4983 Institutional support: RVO:67985840 Keywords : half-linear differential equation * positive solution * asymptotic formula Subject RIV: BA - General Mathematics Impact factor: 0.565, year: 2016 http://projecteuclid.org/euclid.die/1462298681

Application of the successive linear programming technique to the optimum design of a high flux reactor using LEU fuel

International Nuclear Information System (INIS)

Mo, S.C.

1991-01-01

The successive linear programming technique is applied to obtain the optimum thermal flux in the reflector region of a high flux reactor using LEU fuel. The design variables are the reactor power, core radius and coolant channel thickness. The constraints are the cycle length, average heat flux and peak/average power density ratio. The characteristics of the optimum solutions with various constraints are discussed

On Attainability of Optimal Solutions for Linear Elliptic Equations with Unbounded Coefficients

Directory of Open Access Journals (Sweden)

P. I. Kogut

2011-12-01

Full Text Available We study an optimal boundary control problem (OCP associated to a linear elliptic equation —div (Vj/ + A(xVy = f describing diffusion in a turbulent flow. The characteristic feature of this equation is the fact that, in applications, the stream matrix A(x = [a,ij(x]i,j=i,...,N is skew-symmetric, ац(х = —a,ji(x, measurable, and belongs to L -space (rather than L°°. An optimal solution to such problem can inherit a singular character of the original stream matrix A. We show that optimal solutions can be attainable by solutions of special optimal boundary control problems.

Yager’s ranking method for solving the trapezoidal fuzzy number linear programming

Science.gov (United States)

Karyati; Wutsqa, D. U.; Insani, N.

2018-03-01

In the previous research, the authors have studied the fuzzy simplex method for trapezoidal fuzzy number linear programming based on the Maleki’s ranking function. We have found some theories related to the term conditions for the optimum solution of fuzzy simplex method, the fuzzy Big-M method, the fuzzy two-phase method, and the sensitivity analysis. In this research, we study about the fuzzy simplex method based on the other ranking function. It is called Yager's ranking function. In this case, we investigate the optimum term conditions. Based on the result of research, it is found that Yager’s ranking function is not like Maleki’s ranking function. Using the Yager’s function, the simplex method cannot work as well as when using the Maleki’s function. By using the Yager’s function, the value of the subtraction of two equal fuzzy numbers is not equal to zero. This condition makes the optimum table of the fuzzy simplex table is undetected. As a result, the simplified fuzzy simplex table becomes stopped and does not reach the optimum solution.

On the Liouvillian solution of second-order linear differential equations and algebraic invariant curves

International Nuclear Information System (INIS)

Man, Yiu-Kwong

2010-01-01

In this communication, we present a method for computing the Liouvillian solution of second-order linear differential equations via algebraic invariant curves. The main idea is to integrate Kovacic's results on second-order linear differential equations with the Prelle-Singer method for computing first integrals of differential equations. Some examples on using this approach are provided. (fast track communication)

An investigation on the solutions for the linear inverse problem in gamma ray tomography

International Nuclear Information System (INIS)

Araujo, Bruna G.M.; Dantas, Carlos C.; Santos, Valdemir A. dos; Finkler, Christine L.L.; Oliveira, Eric F. de; Melo, Silvio B.; Santos, M. Graca dos

2009-01-01

This paper the results obtained in single beam gamma ray tomography are investigated according to direct problem formulation and the applied solution for the linear system of equations. By image reconstruction based algebraic computational algorithms are used. The sparse under and over-determined linear system of equations was analyzed. Build in functions of Matlab software were applied and optimal solutions were investigate. Experimentally a section of the tube is scanned from various positions and at different angles. The solution, to find the vector of coefficients μ, from the vector of measured p values through the W matrix inversion, constitutes an inverse problem. A industrial tomography process requires a numerical solution of the system of equations. The definition of inverse problem according to Hadmard's is considered and as well the requirement of a well posed problem to find stable solutions. The formulation of the basis function and the computational algorithm to structure the weight matrix W were analyzed. For W full rank matrix the obtained solution is unique as expected. Total Least Squares was implemented which theory and computation algorithm gives adequate treatment for the problems due to non-unique solutions of the system of equations. Stability of the solution was investigating by means of a regularization technique and the comparison shows that it improves the results. An optimal solution as a function of the image quality, computation time and minimum residuals were quantified. The corresponding reconstructed images are shown in 3D graphics in order to compare with the solution. (author)

On oscillations of solutions to second-order linear delay differential equations

Czech Academy of Sciences Publication Activity Database

Opluštil, Z.; Šremr, Jiří

2013-01-01

Roč. 20, č. 1 (2013), s. 65-94 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : linear second-order delay differential equation * oscillatory solution Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-1/gmj-2013-0001/gmj-2013-0001.xml?format=INT

On oscillations of solutions to second-order linear delay differential equations

Czech Academy of Sciences Publication Activity Database

Opluštil, Z.; Šremr, Jiří

2013-01-01

Roč. 20, č. 1 (2013), s. 65-94 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : linear second-order delay differential equation * oscillatory solution Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-1/gmj-2013-0001/gmj-2013-0001. xml ?format=INT

On the stability, the periodic solutions and the resolution of certain types of non linear equations, and of non linearly coupled systems of these equations, appearing in betatronic oscillations

International Nuclear Information System (INIS)

Valat, J.

1960-12-01

Universal stability diagrams have been calculated and experimentally checked for Hill-Meissner type equations with square-wave coefficients. The study of these equations in the phase-plane has then made it possible to extend the periodic solution calculations to the case of non-linear differential equations with periodic square-wave coefficients. This theory has been checked experimentally. For non-linear coupled systems with constant coefficients, a search was first made for solutions giving an algebraic motion. The elliptical and Fuchs's functions solve such motions. The study of non-algebraic motions is more delicate, apart from the study of nonlinear Lissajous's motions. A functional analysis shows that it is possible however in certain cases to decouple the system and to find general solutions. For non-linear coupled systems with periodic square-wave coefficients it is then possible to calculate the conditions leading to periodic solutions, if the two non-linear associated systems with constant coefficients fall into one of the categories of the above paragraph. (author) [fr

Fuzzy linear programming approach for solving transportation

Indian Academy of Sciences (India)

Transportation problem (TP) is an important network structured linear programming problem that arises in several contexts and has deservedly received a great deal of attention in the literature. The central concept in this problem is to find the least total transportation cost of a commodity in order to satisfy demands at ...

Large-scale linear programs in planning and prediction.

Science.gov (United States)

2017-06-01

Large-scale linear programs are at the core of many traffic-related optimization problems in both planning and prediction. Moreover, many of these involve significant uncertainty, and hence are modeled using either chance constraints, or robust optim...

Matlab linear algebra

CERN Document Server

Lopez, Cesar

2014-01-01

MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Linear Algebra introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving an introduction to

International program on linear electric motors

Energy Technology Data Exchange (ETDEWEB)

Dawson, G.E.; Eastham, A.R.; Parker, J.H.

1992-05-01

The International Program on Linear Electric Motors (LEM) was initiated for the purposes of commumication and coordination between various centers of expertise in LEM technology in Germany, Japan and Canada. Furthermore, it was intended to provide assessment and support of the planning of technological developments and for dissemination of information to researchers, service operators and policy makers, and to ensure that full advantage can be taken if opportunities for technology transfer occur. In the process, the program was able to provide closer contacts between researchers, to enhance and encourage collaborative research and development, and to facilitate joint ventures in advanced transportation technologies. Work done under the program is documented, and seminar materials presented by Canadian researchers in Italy, and by Italian researchers at Queen's University in Canada are presented. Five separate abstracts have been prepared for the main body of the report and the seminar materials.

A novel linear programming approach to fluence map optimization for intensity modulated radiation therapy treatment planning

International Nuclear Information System (INIS)

Romeijn, H Edwin; Ahuja, Ravindra K; Dempsey, James F; Kumar, Arvind; Li, Jonathan G

2003-01-01

We present a novel linear programming (LP) based approach for efficiently solving the intensity modulated radiation therapy (IMRT) fluence-map optimization (FMO) problem to global optimality. Our model overcomes the apparent limitations of a linear-programming approach by approximating any convex objective function by a piecewise linear convex function. This approach allows us to retain the flexibility offered by general convex objective functions, while allowing us to formulate the FMO problem as a LP problem. In addition, a novel type of partial-volume constraint that bounds the tail averages of the differential dose-volume histograms of structures is imposed while retaining linearity as an alternative approach to improve dose homogeneity in the target volumes, and to attempt to spare as many critical structures as possible. The goal of this work is to develop a very rapid global optimization approach that finds high quality dose distributions. Implementation of this model has demonstrated excellent results. We found globally optimal solutions for eight 7-beam head-and-neck cases in less than 3 min of computational time on a single processor personal computer without the use of partial-volume constraints. Adding such constraints increased the running times by a factor of 2-3, but improved the sparing of critical structures. All cases demonstrated excellent target coverage (>95%), target homogeneity (<10% overdosing and <7% underdosing) and organ sparing using at least one of the two models

Evaluating forest management policies by parametric linear programing

Science.gov (United States)

Daniel I. Navon; Richard J. McConnen

1967-01-01

An analytical and simulation technique, parametric linear programing explores alternative conditions and devises an optimal management plan for each condition. Its application in solving policy-decision problems in the management of forest lands is illustrated in an example.

Solution of systems of linear algebraic equations by the method of summation of divergent series

International Nuclear Information System (INIS)

Kirichenko, G.A.; Korovin, Ya.S.; Khisamutdinov, M.V.; Shmojlov, V.I.

2015-01-01

A method for solving systems of linear algebraic equations has been proposed on the basis on the summation of the corresponding continued fractions. The proposed algorithm for solving systems of linear algebraic equations is classified as direct algorithms providing an exact solution in a finite number of operations. Examples of solving systems of linear algebraic equations have been presented and the effectiveness of the algorithm has been estimated [ru

Solution strategies for linear and nonlinear instability phenomena for arbitrarily thin shell structures

International Nuclear Information System (INIS)

Eckstein, U.; Harte, R.; Kraetzig, W.B.; Wittek, U.

1983-01-01

In order to describe nonlinear response and instability behaviour the paper starts with the total potential energy considering the basic kinematic equations of a consistent nonlinear shell theory for large displacements and moderate rotations. The material behaviour is assumed to be hyperelastic and isotropic. The incrementation and discretization of the total potential energy leads to the tangent stiffness relation, which is the central equation of computational algorithms based on combined incremental and iterative techniques. Here a symmetrized form of the RIKS/WEMPNER-algorithm for positive and negative load incrementation represents the basis of the nonlinear solution technique. To detect secondary equilibrium branches at points of neutral equilibrium within nonlinear primary paths a quadratic eigenvalue-problem has to be solved. In order to follow those complicated nonlinear response phenomena the RIKS/WEMPNER incrementation/iteration process is combined with a simultaneous solution of the linearized quadratic eigenvalue-problem. Additionally the essentials of a recently derived family of arbitrarily curved shell elements for linear (LACS) and geometrically nonlinear (NACS) shell problems are presented. The main advantage of these elements is the exact description of all geometric properties as well as the energy-equivalent representation of the applied loads in combination with an efficient algorithm to form the stiffness submatrices. Especially the NACS-elements are designed to improve the accuracy of the solution in the deep postbuckling range including moderate rotations. The derived finite elements and solution strategies are applied to a certain number of typical shell problems to prove the precision of the shell elements and to demonstrate the possibilities of tracing linear and nonlinear bifurcation problems as well as snap-through phenomena with and without secondary bifurcation branches. (orig.)

C-program LINOP for the evaluation of film dosemeters by linear optimization. User manual

International Nuclear Information System (INIS)

Kragh, P.

1995-11-01

Linear programming results in an optimal measuring value for film dosemeters. The Linop program was developed to be used for linear programming. The program permits the evaluation and control of film dosemeters and of all other multi-component dosemeters. This user manual for the Linop program contains the source program, a description of the program and installation and use instructions. The data sets with programs and examples are available upon request. (orig.) [de

On the summability of divergent power series solutions for certain first-order linear PDEs

Directory of Open Access Journals (Sweden)

Masaki Hibino

2015-01-01

Full Text Available This article is concerned with the study of the Borel summability of divergent power series solutions for certain singular first-order linear partial differential equations of nilpotent type. Our main purpose is to obtain conditions which coefficients of equations should satisfy in order to ensure the Borel summability of divergent solutions. We will see that there is a close affinity between the Borel summability of divergent solutions and global analytic continuation properties for coefficients of equations.

A property of assignment type mixed integer linear programming problems

NARCIS (Netherlands)

Benders, J.F.; van Nunen, J.A.E.E.

1982-01-01

In this paper we will proof that rather tight upper bounds can be given for the number of non-unique assignments that are achieved after solving the linear programming relaxation of some types of mixed integer linear assignment problems. Since in these cases the number of splitted assignments is

An improved risk-explicit interval linear programming model for pollution load allocation for watershed management.

Science.gov (United States)

Xia, Bisheng; Qian, Xin; Yao, Hong

2017-11-01

Although the risk-explicit interval linear programming (REILP) model has solved the problem of having interval solutions, it has an equity problem, which can lead to unbalanced allocation between different decision variables. Therefore, an improved REILP model is proposed. This model adds an equity objective function and three constraint conditions to overcome this equity problem. In this case, pollution reduction is in proportion to pollutant load, which supports balanced development between different regional economies. The model is used to solve the problem of pollution load allocation in a small transboundary watershed. Compared with the REILP original model result, our model achieves equity between the upstream and downstream pollutant loads; it also overcomes the problem of greatest pollution reduction, where sources are nearest to the control section. The model provides a better solution to the problem of pollution load allocation than previous versions.

Linearly Adjustable International Portfolios

International Nuclear Information System (INIS)

Fonseca, R. J.; Kuhn, D.; Rustem, B.

2010-01-01

We present an approach to multi-stage international portfolio optimization based on the imposition of a linear structure on the recourse decisions. Multiperiod decision problems are traditionally formulated as stochastic programs. Scenario tree based solutions however can become intractable as the number of stages increases. By restricting the space of decision policies to linear rules, we obtain a conservative tractable approximation to the original problem. Local asset prices and foreign exchange rates are modelled separately, which allows for a direct measure of their impact on the final portfolio value.

Linearly Adjustable International Portfolios

Science.gov (United States)

Fonseca, R. J.; Kuhn, D.; Rustem, B.

2010-09-01

We present an approach to multi-stage international portfolio optimization based on the imposition of a linear structure on the recourse decisions. Multiperiod decision problems are traditionally formulated as stochastic programs. Scenario tree based solutions however can become intractable as the number of stages increases. By restricting the space of decision policies to linear rules, we obtain a conservative tractable approximation to the original problem. Local asset prices and foreign exchange rates are modelled separately, which allows for a direct measure of their impact on the final portfolio value.

Linear programming optimization of nuclear energy strategy with sodium-cooled fast reactors

International Nuclear Information System (INIS)

Lee, Je Whan; Jeong, Yong Hoon; Chang, Yoon Il; Chang, Soon Heung

2011-01-01

Nuclear power has become an essential part of electricity generation to meet the continuous growth of electricity demand. A Sodium-cooled Fast Reactor (SFR) was developed to extend uranium resource utilization under a growing nuclear energy scenario while concomitantly providing a nuclear waste management solution. Key questions in this scenario are when to introduce SFRs and how many reactors should be introduced. In this study, a methodology using Linear Programming is employed in order to quantify an optimized growth pattern of a nuclear energy system comprising light water reactors and SFRs. The optimization involves tradeoffs between SFR capital cost premiums and the total system U3O8 price premiums. Optimum nuclear growth patterns for several scenarios are presented, as well as sensitivity analyses of important input parameters

Simple and accurate solution for convective-radiative fin with temperature dependent thermal conductivity using double optimal linearization

International Nuclear Information System (INIS)

Bouaziz, M.N.; Aziz, Abdul

2010-01-01

A novel concept of double optimal linearization is introduced and used to obtain a simple and accurate solution for the temperature distribution in a straight rectangular convective-radiative fin with temperature dependent thermal conductivity. The solution is built from the classical solution for a pure convection fin of constant thermal conductivity which appears in terms of hyperbolic functions. When compared with the direct numerical solution, the double optimally linearized solution is found to be accurate within 4% for a range of radiation-conduction and thermal conductivity parameters that are likely to be encountered in practice. The present solution is simple and offers superior accuracy compared with the fairly complex approximate solutions based on the homotopy perturbation method, variational iteration method, and the double series regular perturbation method. The fin efficiency expression resembles the classical result for the constant thermal conductivity convecting fin. The present results are easily usable by the practicing engineers in their thermal design and analysis work involving fins.

On the completeness of the set of Bethe-Hulthen solutions of the linear Heisenberg system

International Nuclear Information System (INIS)

Caspers, W J; Labuz, M; Wal, A

2006-01-01

In this work we formulate the standard form of the solutions of the Heisenberg chain with periodic boundary conditions and show that these solutions can be transformed into the well-known Bethe-Hulthen solutions. The standard form is found by solving the secular problem, separated according to the irreducible representations of the translation group. The relevant parameters exp(ik j ) of the Bethe-Hulthen solutions are found from a set of linear equations with coefficients derived from the standard solutions. This correspondence between standard and Bethe-Hulthen solutions realizes the completeness of the Bethe-Hulthen method

A Spreadsheet-Based, Matrix Formulation Linear Programming Lesson

DEFF Research Database (Denmark)

Harrod, Steven

2009-01-01

The article focuses on the spreadsheet-based, matrix formulation linear programming lesson. According to the article, it makes a higher level of theoretical mathematics approachable by a wide spectrum of students wherein many may not be decision sciences or quantitative methods majors. Moreover...

New exact solutions of the Tzitzéica-type equations in non-linear optics using the expa function method

Science.gov (United States)

Hosseini, K.; Ayati, Z.; Ansari, R.

2018-04-01

One specific class of non-linear evolution equations, known as the Tzitzéica-type equations, has received great attention from a group of researchers involved in non-linear science. In this article, new exact solutions of the Tzitzéica-type equations arising in non-linear optics, including the Tzitzéica, Dodd-Bullough-Mikhailov and Tzitzéica-Dodd-Bullough equations, are obtained using the expa function method. The integration technique actually suggests a useful and reliable method to extract new exact solutions of a wide range of non-linear evolution equations.

Controller design approach based on linear programming.

Science.gov (United States)

Tanaka, Ryo; Shibasaki, Hiroki; Ogawa, Hiromitsu; Murakami, Takahiro; Ishida, Yoshihisa

2013-11-01

This study explains and demonstrates the design method for a control system with a load disturbance observer. Observer gains are determined by linear programming (LP) in terms of the Routh-Hurwitz stability criterion and the final-value theorem. In addition, the control model has a feedback structure, and feedback gains are determined to be the linear quadratic regulator. The simulation results confirmed that compared with the conventional method, the output estimated by our proposed method converges to a reference input faster when a load disturbance is added to a control system. In addition, we also confirmed the effectiveness of the proposed method by performing an experiment with a DC motor. © 2013 ISA. Published by ISA. All rights reserved.

Spline smoothing of histograms by linear programming

Science.gov (United States)

Bennett, J. O.

1972-01-01

An algorithm for an approximating function to the frequency distribution is obtained from a sample of size n. To obtain the approximating function a histogram is made from the data. Next, Euclidean space approximations to the graph of the histogram using central B-splines as basis elements are obtained by linear programming. The approximating function has area one and is nonnegative.

Oscillation of solutions of some higher order linear differential equations

Directory of Open Access Journals (Sweden)

Hong-Yan Xu

2009-11-01

Full Text Available In this paper, we deal with the order of growth and the hyper order of solutions of higher order linear differential equations $$f^{(k}+B_{k-1}f^{(k-1}+\\cdots+B_1f'+B_0f=F$$ where $B_j(z (j=0,1,\\ldots,k-1$ and $F$ are entire functions or polynomials. Some results are obtained which improve and extend previous results given by Z.-X. Chen, J. Wang, T.-B. Cao and C.-H. Li.

Formulated linear programming problems from game theory and its ...

African Journals Online (AJOL)

Formulated linear programming problems from game theory and its computer implementation using Tora package. ... Game theory, a branch of operations research examines the various concepts of decision ... AJOL African Journals Online.

Exact solutions of linearized Schwinger endash Dyson equation of fermion self-energy

International Nuclear Information System (INIS)

Zhou, B.

1997-01-01

The Schwinger endash Dyson equation of fermion self-energy in the linearization approximation is solved exactly in a theory with gauge and effective four-fermion interactions. Different expressions for the independent solutions, which, respectively, submit to irregular and regular ultraviolet boundary condition are derived and expounded. copyright 1997 American Institute of Physics

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

Positive solution of non-square fully Fuzzy linear system of equation in general form using least square method

Directory of Open Access Journals (Sweden)

Reza Ezzati

2014-08-01

Full Text Available In this paper, we propose the least square method for computing the positive solution of a non-square fully fuzzy linear system. To this end, we use Kaffman' arithmetic operations on fuzzy numbers \\cite{17}. Here, considered existence of exact solution using pseudoinverse, if they are not satisfy in positive solution condition, we will compute fuzzy vector core and then we will obtain right and left spreads of positive fuzzy vector by introducing constrained least squares problem. Using our proposed method, non-square fully fuzzy linear system of equations always has a solution. Finally, we illustrate the efficiency of proposed method by solving some numerical examples.

Periodic inventory system in cafeteria using linear programming

Science.gov (United States)

Usop, Mohd Fais; Ishak, Ruzana; Hamdan, Ahmad Ridhuan

2017-11-01

Inventory management is an important factor in running a business. It plays a big role of managing the stock in cafeteria. If the inventories are failed to be managed wisely, it will affect the profit of the cafeteria. Therefore, the purpose of this study is to find the solution of the inventory management in cafeteria. Most of the cafeteria in Malaysia did not manage their stock well. Therefore, this study is to propose a database system of inventory management and to develop the inventory model in cafeteria management. In this study, new database system to improve the management of the stock in a weekly basis will be provided using Linear Programming Model to get the optimal range of the inventory needed for selected categories. Data that were collected by using the Periodic Inventory System at the end of the week within three months period being analyzed by using the Food Stock-take Database. The inventory model was developed from the collected data according to the category of the inventory in the cafeteria. Results showed the effectiveness of using the Periodic Inventory System and will be very helpful to the cafeteria management in organizing the inventory. Moreover, the findings in this study can reduce the cost of operation and increased the profit.

Bounded solutions of self-adjoint second order linear difference equations with periodic coeffients

Directory of Open Access Journals (Sweden)

Encinas A.M.

2018-02-01

Full Text Available In this work we obtain easy characterizations for the boundedness of the solutions of the discrete, self–adjoint, second order and linear unidimensional equations with periodic coefficients, including the analysis of the so-called discrete Mathieu equations as particular cases.

MAGDM linear-programming models with distinct uncertain preference structures.

Science.gov (United States)

Xu, Zeshui S; Chen, Jian

2008-10-01

Group decision making with preference information on alternatives is an interesting and important research topic which has been receiving more and more attention in recent years. The purpose of this paper is to investigate multiple-attribute group decision-making (MAGDM) problems with distinct uncertain preference structures. We develop some linear-programming models for dealing with the MAGDM problems, where the information about attribute weights is incomplete, and the decision makers have their preferences on alternatives. The provided preference information can be represented in the following three distinct uncertain preference structures: 1) interval utility values; 2) interval fuzzy preference relations; and 3) interval multiplicative preference relations. We first establish some linear-programming models based on decision matrix and each of the distinct uncertain preference structures and, then, develop some linear-programming models to integrate all three structures of subjective uncertain preference information provided by the decision makers and the objective information depicted in the decision matrix. Furthermore, we propose a simple and straightforward approach in ranking and selecting the given alternatives. It is worth pointing out that the developed models can also be used to deal with the situations where the three distinct uncertain preference structures are reduced to the traditional ones, i.e., utility values, fuzzy preference relations, and multiplicative preference relations. Finally, we use a practical example to illustrate in detail the calculation process of the developed approach.

Fall with linear drag and Wien's displacement law: approximate solution and Lambert function

International Nuclear Information System (INIS)

Vial, Alexandre

2012-01-01

We present an approximate solution for the downward time of travel in the case of a mass falling with a linear drag force. We show how a quasi-analytical solution implying the Lambert function can be found. We also show that solving the previous problem is equivalent to the search for Wien's displacement law. These results can be of interest for undergraduate students, as they show that some transcendental equations found in physics may be solved without purely numerical methods. Moreover, as will be seen in the case of Wien's displacement law, solutions based on series expansion can be very accurate even with few terms. (paper)

Accommodation of practical constraints by a linear programming jet select. [for Space Shuttle

Science.gov (United States)

Bergmann, E.; Weiler, P.

1983-01-01

An experimental spacecraft control system will be incorporated into the Space Shuttle flight software and exercised during a forthcoming mission to evaluate its performance and handling qualities. The control system incorporates a 'phase space' control law to generate rate change requests and a linear programming jet select to compute jet firings. Posed as a linear programming problem, jet selection must represent the rate change request as a linear combination of jet acceleration vectors where the coefficients are the jet firing times, while minimizing the fuel expended in satisfying that request. This problem is solved in real time using a revised Simplex algorithm. In order to implement the jet selection algorithm in the Shuttle flight control computer, it was modified to accommodate certain practical features of the Shuttle such as limited computer throughput, lengthy firing times, and a large number of control jets. To the authors' knowledge, this is the first such application of linear programming. It was made possible by careful consideration of the jet selection problem in terms of the properties of linear programming and the Simplex algorithm. These modifications to the jet select algorithm may by useful for the design of reaction controlled spacecraft.

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.

Direct interaction between linear electron transfer chains and solute transport systems in bacteria

NARCIS (Netherlands)

Elferink, Marieke G.L.; Hellingwerf, Klaas J.; Belkum, Marco J. van; Poolman, Bert; Konings, Wil N.

1984-01-01

In studies on alanine and lactose transport in Rhodopseudomonas sphaeroides we have demonstrated that the rate of solute uptake in this phototrophic bacterium is regulated by the rate of light-induced cyclic electron transfer. In the present paper the interaction between linear electron transfer

Linear Motor for Drive of Belt Conveyor

Directory of Open Access Journals (Sweden)

Milan Krasl

2006-01-01

Full Text Available This paper introduces a novel approach on the design of a linear motor for drive of belt conveyor (LMBC. The motor is a simple combination of asynchronous motor in plane. The electromagnetic forces is one of the most important parameters of electrical machines. This parameter is necessary for the checking of the design. This paper describes several variants: linear motor with slots in platens, slots in one half of platens and optimization of slots. The electromagnetic force can be found with the help of a Finite Elements Method – based program. For solution was used QuickField program.

Remark on zeros of solutions of second-order linear ordinary differential equations

Czech Academy of Sciences Publication Activity Database

Dosoudilová, M.; Lomtatidze, Alexander

2016-01-01

Roč. 23, č. 4 (2016), s. 571-577 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : second-order linear equation * zeros of solutions * periodic boundary value problem Subject RIV: BA - General Mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2016.23.issue-4/gmj-2016-0052/gmj-2016-0052. xml

Remark on zeros of solutions of second-order linear ordinary differential equations

Czech Academy of Sciences Publication Activity Database

Dosoudilová, M.; Lomtatidze, Alexander

2016-01-01

Roč. 23, č. 4 (2016), s. 571-577 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : second-order linear equation * zero s of solutions * periodic boundary value problem Subject RIV: BA - General Mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2016.23.issue-4/gmj-2016-0052/gmj-2016-0052.xml

A General Construction of Linear Differential Equations with Solutions of Prescribed Properties

Czech Academy of Sciences Publication Activity Database

Neuman, František

2004-01-01

Roč. 17, č. 1 (2004), s. 71-76 ISSN 0893-9659 R&D Projects: GA AV ČR IAA1019902; GA ČR GA201/99/0295 Institutional research plan: CEZ:AV0Z1019905 Keywords : construction of linear differential equations * prescribed qualitative properties of solutions Subject RIV: BA - General Mathematics Impact factor: 0.414, year: 2004

High Order A-stable Continuous General Linear Methods for Solution of Systems of Initial Value Problems in ODEs

Directory of Open Access Journals (Sweden)

Dauda GuliburYAKUBU

2012-12-01

Full Text Available Accurate solutions to initial value systems of ordinary differential equations may be approximated efficiently by Runge-Kutta methods or linear multistep methods. Each of these has limitations of one sort or another. In this paper we consider, as a middle ground, the derivation of continuous general linear methods for solution of stiff systems of initial value problems in ordinary differential equations. These methods are designed to combine the advantages of both Runge-Kutta and linear multistep methods. Particularly, methods possessing the property of A-stability are identified as promising methods within this large class of general linear methods. We show that the continuous general linear methods are self-starting and have more ability to solve the stiff systems of ordinary differential equations, than the discrete ones. The initial value systems of ordinary differential equations are solved, for instance, without looking for any other method to start the integration process. This desirable feature of the proposed approach leads to obtaining very high accuracy of the solution of the given problem. Illustrative examples are given to demonstrate the novelty and reliability of the methods.

The numerical solution of linear multi-term fractional differential equations: systems of equations

Science.gov (United States)

Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

2002-11-01

In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

Piecewise linear emulator of the nonlinear Schroedinger equation and the resulting analytic solutions for Bose-Einstein condensates

International Nuclear Information System (INIS)

Theodorakis, Stavros

2003-01-01

We emulate the cubic term Ψ 3 in the nonlinear Schroedinger equation by a piecewise linear term, thus reducing the problem to a set of uncoupled linear inhomogeneous differential equations. The resulting analytic expressions constitute an excellent approximation to the exact solutions, as is explicitly shown in the case of the kink, the vortex, and a δ function trap. Such a piecewise linear emulation can be used for any differential equation where the only nonlinearity is a Ψ 3 one. In particular, it can be used for the nonlinear Schroedinger equation in the presence of harmonic traps, giving analytic Bose-Einstein condensate solutions that reproduce very accurately the numerically calculated ones in one, two, and three dimensions

International program on linear electric motors. CIGGT report No. 92-1

Energy Technology Data Exchange (ETDEWEB)

Dawson, G.E.; Eastham, A.R.; Parker, J.H.

1992-12-31

The International Program for Linear Electric Motors (LEM) was begun in April 1989 to communicate and coordinate activities with centers of expertise in Germany, Canada, and Japan; to provide for the assessment and support of the planning of technological developments and for dissemination of information to researchers, service operators, and policy makers; and to ensure that full advantage can be taken if opportunities for technology transfer occur. This report documents the work done under the program, including standardizing linear induction motor (LIM) design characteristics; test procedures and measurement methods; rating; database for design data; criteria for evaluation of designs; computer programs for modelling performance; and a design study for an agreed application.

Indirect synthesis of multi-degree of freedom transient systems. [linear programming for a kinematically linear system

Science.gov (United States)

Pilkey, W. D.; Chen, Y. H.

1974-01-01

An indirect synthesis method is used in the efficient optimal design of multi-degree of freedom, multi-design element, nonlinear, transient systems. A limiting performance analysis which requires linear programming for a kinematically linear system is presented. The system is selected using system identification methods such that the designed system responds as closely as possible to the limiting performance. The efficiency is a result of the method avoiding the repetitive systems analyses accompanying other numerical optimization methods.

Localized and periodic exact solutions to the nonlinear Schroedinger equation with spatially modulated parameters: Linear and nonlinear lattices

International Nuclear Information System (INIS)

Belmonte-Beitia, Juan; Konotop, Vladimir V.; Perez-Garcia, Victor M.; Vekslerchik, Vadym E.

2009-01-01

Using similarity transformations we construct explicit solutions of the nonlinear Schroedinger equation with linear and nonlinear periodic potentials. We present explicit forms of spatially localized and periodic solutions, and study their properties. We put our results in the framework of the exploited perturbation techniques and discuss their implications on the properties of associated linear periodic potentials and on the possibilities of stabilization of gap solitons using polychromatic lattices.

Stationary solution of the Fokker-Planck equation for linearly coupled motion in an electron storage ring

International Nuclear Information System (INIS)

Chao, A.W.; Lee, M.J.

1975-09-01

Effects upon longitudinal bunch shape in a storage ring due to linear and nonlinear potential can be calculated by finding the stationary solution to the Fokker-Planck equation for the particle distribution. Effects upon transverse bunch shape of a stored electron beam due to photon emissions and damping can be calculated by this method. It has been found that this method can also be used for a case in which the transverse modes of oscillation are coupled to the energy deviation δ. Examples of lattice elements which produce linear coupling between these oscillations are skew quadrupole magnets and solenoid magnets. For the linearly coupled case the stationary solution has been found to be given by exp (ΣΣA/sub ij/ x/sub i/x/sub j/) with x/sub i/ the canonical variables (x,p/sub x/, y, p/sub y/, δ, p/sub δ/) and A /sub ij/ some constants. The solution for the values of A /sub ij/'s will be described in this report. It will be shown that this solution can be expressed in a compact form. For simple cases, this form of solution leads directly to analytic expressions for the values of A /sub ij/'s and the bunch shape can be calculated by integrating the distribution function over some of the coordinates; for the more complex cases, it can be conveniently adapted as an algorithm for numerical evaluation. 16 refs

Value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations

Directory of Open Access Journals (Sweden)

Luo Li-Qin

2016-01-01

Full Text Available In this paper, we investigate the value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations, and obtain the results on the relations between the order of the solutions and the convergence exponents of the zeros, poles, a-points and small function value points of the solutions, which show the relations in the case of non-homogeneous equations are sharper than the ones in the case of homogeneous equations.

LCPT: a program for finding linear canonical transformations

International Nuclear Information System (INIS)

Char, B.W.; McNamara, B.

1979-01-01

This article describes a MACSYMA program to compute symbolically a canonical linear transformation between coordinate systems. The difficulties in implementation of this canonical small physics problem are also discussed, along with the implications that may be drawn from such difficulties about widespread MACSYMA usage by the community of computational/theoretical physicists

Interior-Point Methods for Linear Programming: A Review

Science.gov (United States)

Singh, J. N.; Singh, D.

2002-01-01

The paper reviews some recent advances in interior-point methods for linear programming and indicates directions in which future progress can be made. Most of the interior-point methods belong to any of three categories: affine-scaling methods, potential reduction methods and central path methods. These methods are discussed together with…

Optimization for decision making linear and quadratic models

CERN Document Server

Murty, Katta G

2010-01-01

While maintaining the rigorous linear programming instruction required, Murty's new book is unique in its focus on developing modeling skills to support valid decision-making for complex real world problems, and includes solutions to brand new algorithms.

On the solution of a class of fuzzy system of linear equations

Indian Academy of Sciences (India)

J. Mathematics and Comput. Sci. 1: 1–5. Salkuyeh D K 2011 On the solution of the fuzzy Sylvester matrix equation. Soft Computing 15: 953–961. Senthilkumar P and Rajendran G 2011 New approach to solve symmetric fully fuzzy linear systems. S¯adhan¯a 36: 933–940. Wang K and Zheng B 2007 Block iterative methods ...

Higher derivative discontinuous solutions to linear ordinary differential equations: a new route to complexity?

International Nuclear Information System (INIS)

Datta, Dhurjati Prasad; Bose, Manoj Kumar

2004-01-01

We present a new one parameter family of second derivative discontinuous solutions to the simplest scale invariant linear ordinary differential equation. We also point out how the construction could be extended to generate families of higher derivative discontinuous solutions as well. The discontinuity can occur only for a subset of even order derivatives, viz., 2nd, 4th, 8th, 16th,.... The solutions are shown to break the discrete parity (reflection) symmetry of the underlying equation. These results are expected to gain significance in the contemporary search of a new dynamical principle for understanding complex phenomena in nature

Accelerated solution of non-linear flow problems using Chebyshev iteration polynomial based RK recursions

Energy Technology Data Exchange (ETDEWEB)

Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H. [Univ. of Texas, Austin, TX (United States)

1996-12-31

The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.

A parallel solver for huge dense linear systems

Science.gov (United States)

Badia, J. M.; Movilla, J. L.; Climente, J. I.; Castillo, M.; Marqués, M.; Mayo, R.; Quintana-Ortí, E. S.; Planelles, J.

2011-11-01

HDSS (Huge Dense Linear System Solver) is a Fortran Application Programming Interface (API) to facilitate the parallel solution of very large dense systems to scientists and engineers. The API makes use of parallelism to yield an efficient solution of the systems on a wide range of parallel platforms, from clusters of processors to massively parallel multiprocessors. It exploits out-of-core strategies to leverage the secondary memory in order to solve huge linear systems O(100.000). The API is based on the parallel linear algebra library PLAPACK, and on its Out-Of-Core (OOC) extension POOCLAPACK. Both PLAPACK and POOCLAPACK use the Message Passing Interface (MPI) as the communication layer and BLAS to perform the local matrix operations. The API provides a friendly interface to the users, hiding almost all the technical aspects related to the parallel execution of the code and the use of the secondary memory to solve the systems. In particular, the API can automatically select the best way to store and solve the systems, depending of the dimension of the system, the number of processes and the main memory of the platform. Experimental results on several parallel platforms report high performance, reaching more than 1 TFLOP with 64 cores to solve a system with more than 200 000 equations and more than 10 000 right-hand side vectors. New version program summaryProgram title: Huge Dense System Solver (HDSS) Catalogue identifier: AEHU_v1_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHU_v1_1.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.: 87 062 No. of bytes in distributed program, including test data, etc.: 1 069 110 Distribution format: tar.gz Programming language: Fortran90, C Computer: Parallel architectures: multiprocessors, computer clusters Operating system

Spherically symmetric analysis on open FLRW solution in non-linear massive gravity

Energy Technology Data Exchange (ETDEWEB)

Chiang, Chien-I; Izumi, Keisuke; Chen, Pisin, E-mail: chienichiang@berkeley.edu, E-mail: izumi@phys.ntu.edu.tw, E-mail: chen@slac.stanford.edu [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan (China)

2012-12-01

We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The non-linear form of the effective energy-momentum tensor stemming from the mass term is derived for the spherically symmetric case. Only in the special case where the area of the two sphere is not deviated away from the FLRW universe, the effective energy momentum tensor becomes completely the same as that of cosmological constant. This opens a window for discriminating the non-linear massive gravity from general relativity (GR). Indeed, by further solving these spherically symmetric gravitational equations of motion in vacuum to the linear order, we obtain a solution which has an arbitrary time-dependent parameter. In GR, this parameter is a constant and corresponds to the mass of a star. Our result means that Birkhoff's theorem no longer holds in the non-linear massive gravity and suggests that energy can probably be emitted superluminously (with infinite speed) on the self-accelerating background by the helicity-0 mode, which could be a potential plague of this theory.

A Comparison of Traditional Worksheet and Linear Programming Methods for Teaching Manure Application Planning.

Science.gov (United States)

Schmitt, M. A.; And Others

1994-01-01

Compares traditional manure application planning techniques calculated to meet agronomic nutrient needs on a field-by-field basis with plans developed using computer-assisted linear programming optimization methods. Linear programming provided the most economical and environmentally sound manure application strategy. (Contains 15 references.) (MDH)

Planning Student Flow with Linear Programming: A Tunisian Case Study.

Science.gov (United States)

Bezeau, Lawrence

A student flow model in linear programming format, designed to plan the movement of students into secondary and university programs in Tunisia, is described. The purpose of the plan is to determine a sufficient number of graduating students that would flow back into the system as teachers or move into the labor market to meet fixed manpower…

Application of linear programming and perturbation theory in optimization of fuel utilization in a nuclear reactor

International Nuclear Information System (INIS)

Zavaljevski, N.

1985-01-01

Proposed optimization procedure is fast due to application of linear programming. Non-linear constraints which demand iterative application of linear programming are slowing down the calculation. Linearization can be done by different procedures starting from simple empirical rules for fuel in-core management to complicated general perturbation theory with higher order of corrections. A mathematical model was formulated for optimization of improved fuel cycle. A detailed algorithm for determining minimum of fresh fuel at the beginning of each fuel cycle is shown and the problem is linearized by first order perturbation theory and it is optimized by linear programming. Numerical illustration of the proposed method was done for the experimental reactor mostly for saving computer time

Food choices to meet nutrient recommendations for the adult Brazilian population based on the linear programming approach.

Science.gov (United States)

Dos Santos, Quenia; Sichieri, Rosely; Darmon, Nicole; Maillot, Matthieu; Verly-Junior, Eliseu

2018-06-01

To identify optimal food choices that meet nutritional recommendations to reduce prevalence of inadequate nutrient intakes. Linear programming was used to obtain an optimized diet with sixty-eight foods with the least difference from the observed population mean dietary intake while meeting a set of nutritional goals that included reduction in the prevalence of inadequate nutrient intakes to ≤20 %. Brazil. Participants (men and women, n 25 324) aged 20 years or more from the first National Dietary Survey (NDS) 2008-2009. Feasible solution to the model was not found when all constraints were imposed; infeasible nutrients were Ca, vitamins D and E, Mg, Zn, fibre, linolenic acid, monounsaturated fat and Na. Feasible solution was obtained after relaxing the nutritional constraints for these limiting nutrients by including a deviation variable in the model. Estimated prevalence of nutrient inadequacy was reduced by 60-70 % for most nutrients, and mean saturated and trans-fat decreased in the optimized diet meeting the model constraints. Optimized diet was characterized by increases especially in fruits (+92 g), beans (+64 g), vegetables (+43 g), milk (+12 g), fish and seafood (+15 g) and whole cereals (+14 g), and reductions of sugar-sweetened beverages (-90 g), rice (-63 g), snacks (-14 g), red meat (-13 g) and processed meat (-9·7 g). Linear programming is a unique tool to identify which changes in the current diet can increase nutrient intake and place the population at lower risk of nutrient inadequacy. Reaching nutritional adequacy for all nutrients would require major dietary changes in the Brazilian diet.

A Nutritional Analysis of the Food Basket in BIH: A Linear Programming Approach

Directory of Open Access Journals (Sweden)

Arnaut-Berilo Almira

2017-04-01

Full Text Available This paper presents linear and goal programming optimization models for determining and analyzing the food basket in Bosnia and Herzegovina (BiH in terms of adequate nutritional needs according to World Health Organization (WHO standards and World Bank (WB recommendations. A linear programming (LP model and goal linear programming model (GLP are adequate since price and nutrient contents are linearly related to food weight. The LP model provides information about the minimal value and the structure of the food basket for an average person in BiH based on nutrient needs. GLP models are designed to give us information on minimal deviations from nutrient needs if the budget is fixed. Based on these results, poverty analysis can be performed. The data used for the models consisted of 158 food items from the general consumption of the population of BiH according to COICOP classifications, with average prices in 2015 for these products.

A Fast Condensing Method for Solution of Linear-Quadratic Control Problems

DEFF Research Database (Denmark)

Frison, Gianluca; Jørgensen, John Bagterp

2013-01-01

consider a condensing (or state elimination) method to solve an extended version of the LQ control problem, and we show how to exploit the structure of this problem to both factorize the dense Hessian matrix and solve the system. Furthermore, we present two efficient implementations. The first......In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is usually the main computational effort. In this paper we...... implementation is formally identical to the Riccati recursion based solver and has a computational complexity that is linear in the control horizon length and cubic in the number of states. The second implementation has a computational complexity that is quadratic in the control horizon length as well...

Bounds and maximum principles for the solution of the linear transport equation

International Nuclear Information System (INIS)

Larsen, E.W.

1981-01-01

Pointwise bounds are derived for the solution of time-independent linear transport problems with surface sources in convex spatial domains. Under specified conditions, upper bounds are derived which, as a function of position, decrease with distance from the boundary. Also, sufficient conditions are obtained for the existence of maximum and minimum principles, and a counterexample is given which shows that such principles do not always exist

Optimal selection for shielding materials by fuzzy linear programming

International Nuclear Information System (INIS)

Kanai, Y.; Miura, N.; Sugasawa, S.

1996-01-01

An application of fuzzy linear programming methods to optimization of a radiation shield is presented. The main purpose of the present study is the choice of materials and the search of the ratio of mixture-component as the first stage of the methodology on optimum shielding design according to individual requirements of nuclear reactor, reprocessing facility, shipping cask installing spent fuel, ect. The characteristic values for the shield optimization may be considered their cost, spatial space, weight and some shielding qualities such as activation rate and total dose rate for neutron and gamma ray (includes secondary gamma ray). This new approach can reduce huge combination calculations for conventional two-valued logic approaches to representative single shielding calculation by group-wised optimization parameters determined in advance. Using the fuzzy linear programming method, possibilities for reducing radiation effects attainable in optimal compositions hydrated, lead- and boron-contained materials are investigated

Generic Mathematical Programming Formulation and Solution for Computer-Aided Molecular Design

DEFF Research Database (Denmark)

Zhang, Lei; Cignitti, Stefano; Gani, Rafiqul

2015-01-01

This short communication presents a generic mathematical programming formulation for Computer-Aided Molecular Design (CAMD). A given CAMD problem, based on target properties, is formulated as a Mixed Integer Linear/Non-Linear Program (MILP/MINLP). The mathematical programming model presented here......, which is formulated as an MILP/MINLP problem, considers first-order and second-order molecular groups for molecular structure representation and property estimation. It is shown that various CAMD problems can be formulated and solved through this model....

SOILSOLN: A Program for Teaching Equilibria Modeling of Soil Solution Composition.

Science.gov (United States)

Wolt, Jeffrey D.

1989-01-01

Presents a computer program for use in teaching ion speciation in soil solutions. Provides information on the structure of the program, execution, and software specifications. The program estimates concentrations of ion pairs, hydrolytic species, metal-organic complexes, and free ions in solutions. (Author/RT)

Calculations of stationary solutions for the non linear viscous resistive MHD equations in slab geometry

International Nuclear Information System (INIS)

Edery, D.

1983-11-01

The reduced system of the non linear resistive MHD equations is used in the 2-D one helicity approximation in the numerical computations of stationary tearing modes. The critical magnetic Raynolds number S (S=tausub(r)/tausub(H) where tausub(R) and tausub(H) are respectively the characteristic resistive and hydro magnetic times) and the corresponding linear solution are computed as a starting approximation for the full non linear equations. These equations are then treated numerically by an iterative procedure which is shown to be rapidly convergent. A numerical application is given in the last part of this paper

Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation

Science.gov (United States)

Lin, Yu-Chu; Wang, Haitao; Wu, Kung-Chien

2018-04-01

We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad's angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543-1608, 2004), (Bull Inst Math Acad Sin 1:1-78, 2006), (Bull Inst Math Acad Sin 6:151-243, 2011) and Lee et al. (Commun Math Phys 269:17-37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.

Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation

Science.gov (United States)

Lin, Yu-Chu; Wang, Haitao; Wu, Kung-Chien

2018-06-01

We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad's angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543-1608, 2004), (Bull Inst Math Acad Sin 1:1-78, 2006), (Bull Inst Math Acad Sin 6:151-243, 2011) and Lee et al. (Commun Math Phys 269:17-37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.

Non linear Euler-Poisson system. Part 1: global existence of low entropy solutions

International Nuclear Information System (INIS)

Cordier, S.

1995-05-01

In this work a 1-D model of electrons and ions plasma is considered. Electrons are supposed to be in Maxwell-Boltzmann thermodynamic equilibrium while ions are described with an isothermal flow model of charged particles submitted to a self-consistent electric field. A collision term between neutral particles and ions simulates the presence of neutral particles. This work demonstrates the existence of low entropy solutions for this simple model with arbitrary initial conditions. Most of the paper is devoted to the demonstration of this theorem and follows the successive steps: construction of a numerical scheme, recall of the classical properties of Riemann problem solutions using Glimm method, uniform estimations for the whole variation norm, and finally, convergence of the constructed solutions towards a low entropy solution for the non-linear Euler/Poisson system. Domains of application for this type of model are listed in the conclusion. (J.S.). 18 refs

Path integral solution of linear second order partial differential equations I: the general construction

International Nuclear Information System (INIS)

LaChapelle, J.

2004-01-01

A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions. The general solution can be specialized to solve elliptic, parabolic, and hyperbolic partial differential equations with boundary conditions. This extends the well-known path integral solution of the Schroedinger/diffusion equation in unbounded space. The construction is based on a framework for functional integration introduced by Cartier/DeWitt-Morette

Linear Programming, the Simplex Algorithm and Simple Polytopes

Directory of Open Access Journals (Sweden)

Das Bhusan

2010-09-01

Full Text Available In the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concurring the simplex algorithm. We describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes.

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

175 Years of Linear Programming - Minimax and Cake Topography

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 7. 175 Years of Linear Programming - Minimax and Cake Topography. Vijay Chandru M R Rao. Series Article Volume 4 Issue 7 July 1999 pp 4-13. Fulltext. Click here to view fulltext PDF. Permanent link:

SOLUTION OF A MULTIVARIATE STRATIFIED SAMPLING PROBLEM THROUGH CHEBYSHEV GOAL PROGRAMMING

Directory of Open Access Journals (Sweden)

Mohd. Vaseem Ismail

2010-12-01

Full Text Available In this paper, we consider the problem of minimizing the variances for the various characters with fixed (given budget. Each convex objective function is first linearised at its minimal point where it meets the linear cost constraint. The resulting multiobjective linear programming problem is then solved by Chebyshev goal programming. A numerical example is given to illustrate the procedure.

An efficient parallel algorithm for the solution of a tridiagonal linear system of equations

Science.gov (United States)

Stone, H. S.

1971-01-01

Tridiagonal linear systems of equations are solved on conventional serial machines in a time proportional to N, where N is the number of equations. The conventional algorithms do not lend themselves directly to parallel computations on computers of the ILLIAC IV class, in the sense that they appear to be inherently serial. An efficient parallel algorithm is presented in which computation time grows as log sub 2 N. The algorithm is based on recursive doubling solutions of linear recurrence relations, and can be used to solve recurrence relations of all orders.

A time-domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems

Science.gov (United States)

Heinkenschloss, Matthias

2005-01-01

We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.

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

Assembling networks of microbial genomes using linear programming.

Science.gov (United States)

Holloway, Catherine; Beiko, Robert G

2010-11-20

Microbial genomes exhibit complex sets of genetic affinities due to lateral genetic transfer. Assessing the relative contributions of parent-to-offspring inheritance and gene sharing is a vital step in understanding the evolutionary origins and modern-day function of an organism, but recovering and showing these relationships is a challenging problem. We have developed a new approach that uses linear programming to find between-genome relationships, by treating tables of genetic affinities (here, represented by transformed BLAST e-values) as an optimization problem. Validation trials on simulated data demonstrate the effectiveness of the approach in recovering and representing vertical and lateral relationships among genomes. Application of the technique to a set comprising Aquifex aeolicus and 75 other thermophiles showed an important role for large genomes as 'hubs' in the gene sharing network, and suggested that genes are preferentially shared between organisms with similar optimal growth temperatures. We were also able to discover distinct and common genetic contributors to each sequenced representative of genus Pseudomonas. The linear programming approach we have developed can serve as an effective inference tool in its own right, and can be an efficient first step in a more-intensive phylogenomic analysis.

Optimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networks

KAUST Repository

Li, Yanning

2014-03-01

This article presents a new optimal control framework for transportation networks in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi (H-J) equation and the commonly used triangular fundamental diagram, we pose the problem of controlling the state of the system on a network link, in a finite horizon, as a Linear Program (LP). We then show that this framework can be extended to an arbitrary transportation network, resulting in an LP or a Quadratic Program. Unlike many previously investigated transportation network control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e., discontinuities in the state of the system). As it leverages the intrinsic properties of the H-J equation used to model the state of the system, it does not require any approximation, unlike classical methods that are based on discretizations of the model. The computational efficiency of the method is illustrated on a transportation network. © 2014 IEEE.

Optimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networks

KAUST Repository

Li, Yanning; Canepa, Edward S.; Claudel, Christian

2014-01-01

This article presents a new optimal control framework for transportation networks in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi (H-J) equation and the commonly used triangular fundamental diagram, we pose the problem of controlling the state of the system on a network link, in a finite horizon, as a Linear Program (LP). We then show that this framework can be extended to an arbitrary transportation network, resulting in an LP or a Quadratic Program. Unlike many previously investigated transportation network control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e., discontinuities in the state of the system). As it leverages the intrinsic properties of the H-J equation used to model the state of the system, it does not require any approximation, unlike classical methods that are based on discretizations of the model. The computational efficiency of the method is illustrated on a transportation network. © 2014 IEEE.

On the asymptotic expansions of solutions of an nth order linear differential equation with power coefficients

International Nuclear Information System (INIS)

Paris, R.B.; Wood, A.D.

1984-11-01

The asymptotic expansions of solutions of a class of linear ordinary differential equations of arbitrary order n, containing a factor zsup(m) multiplying the lower order derivatives, are investigated for large values of z in the complex plane. Four classes of solutions are considered which exhibit the following behaviour as /z/ → infinity in certain sectors: (i) solutions whose behaviour is either exponentially large or algebraic (involving p ( < n) algebraic expansions), (ii) solutions which are exponentially small (iii) solutions with a single algebraic expansion and (iv) solutions which are even and odd functions of z whenever n+m is even. The asymptotic expansions of these solutions in a full neigbourhood of the point at infinity are obtained by means of the theory of the solutions in the case m=O developed in a previous paper

Solutions to the linearized Navier-Stokes equations for channel flow via the WKB approximation

Science.gov (United States)

Leonard, Anthony

2017-11-01

Progress on determining semi-analytical solutions to the linearized Navier-Stokes equations for incompressible channel flow, laminar and turbulent, is reported. Use of the WKB approximation yields, e.g., solutions to initial-value problem for the inviscid Orr-Sommerfeld equation in terms of the Bessel functions J+ 1 / 3 ,J- 1 / 3 ,J1 , and Y1 and their modified counterparts for any given wave speed c = ω /kx and k⊥ ,(k⊥2 =kx2 +kz2) . Of particular note to be discussed is a sequence i = 1 , 2 , . . . of homogeneous inviscid solutions with complex k⊥ i for each speed c, (0 < c <=Umax), in the downstream direction. These solutions for the velocity component normal to the wall v are localized in the plane parallel to the wall. In addition, for limited range of negative c, (- c * <= c <= 0) , we have found upstream-traveling homogeneous solutions with real k⊥(c) . In both cases the solutions for v serve as a source for corresponding solutions to the inviscid Squire equation for the vorticity component normal to the wall ωy.

A simple model for electrical charge in globular macromolecules and linear polyelectrolytes in solution

Science.gov (United States)

Krishnan, M.

2017-05-01

We present a model for calculating the net and effective electrical charge of globular macromolecules and linear polyelectrolytes such as proteins and DNA, given the concentration of monovalent salt and pH in solution. The calculation is based on a numerical solution of the non-linear Poisson-Boltzmann equation using a finite element discretized continuum approach. The model simultaneously addresses the phenomena of charge regulation and renormalization, both of which underpin the electrostatics of biomolecules in solution. We show that while charge regulation addresses the true electrical charge of a molecule arising from the acid-base equilibria of its ionizable groups, charge renormalization finds relevance in the context of a molecule's interaction with another charged entity. Writing this electrostatic interaction free energy in terms of a local electrical potential, we obtain an "interaction charge" for the molecule which we demonstrate agrees closely with the "effective charge" discussed in charge renormalization and counterion-condensation theories. The predictions of this model agree well with direct high-precision measurements of effective electrical charge of polyelectrolytes such as nucleic acids and disordered proteins in solution, without tunable parameters. Including the effective interior dielectric constant for compactly folded molecules as a tunable parameter, the model captures measurements of effective charge as well as published trends of pKa shifts in globular proteins. Our results suggest a straightforward general framework to model electrostatics in biomolecules in solution. In offering a platform that directly links theory and experiment, these calculations could foster a systematic understanding of the interrelationship between molecular 3D structure and conformation, electrical charge and electrostatic interactions in solution. The model could find particular relevance in situations where molecular crystal structures are not available or

Algorithmic Trading with Developmental and Linear Genetic Programming

Science.gov (United States)

Wilson, Garnett; Banzhaf, Wolfgang

A developmental co-evolutionary genetic programming approach (PAM DGP) and a standard linear genetic programming (LGP) stock trading systemare applied to a number of stocks across market sectors. Both GP techniques were found to be robust to market fluctuations and reactive to opportunities associated with stock price rise and fall, with PAMDGP generating notably greater profit in some stock trend scenarios. Both algorithms were very accurate at buying to achieve profit and selling to protect assets, while exhibiting bothmoderate trading activity and the ability to maximize or minimize investment as appropriate. The content of the trading rules produced by both algorithms are also examined in relation to stock price trend scenarios.

Optimal Airport Surface Traffic Planning Using Mixed-Integer Linear Programming

Directory of Open Access Journals (Sweden)

P. C. Roling

2008-01-01

Full Text Available We describe an ongoing research effort pertaining to the development of a surface traffic automation system that will help controllers to better coordinate surface traffic movements related to arrival and departure traffic. More specifically, we describe the concept for a taxi-planning support tool that aims to optimize the routing and scheduling of airport surface traffic in such a way as to deconflict the taxi plans while optimizing delay, total taxi-time, or some other airport efficiency metric. Certain input parameters related to resource demand, such as the expected landing times and the expected pushback times, are rather difficult to predict accurately. Due to uncertainty in the input data driving the taxi-planning process, the taxi-planning tool is designed such that it produces solutions that are robust to uncertainty. The taxi-planning concept presented herein, which is based on mixed-integer linear programming, is designed such that it is able to adapt to perturbations in these input conditions, as well as to account for failure in the actual execution of surface trajectories. The capabilities of the tool are illustrated in a simple hypothetical airport.

Convergence Guaranteed Nonlinear Constraint Model Predictive Control via I/O Linearization

Directory of Open Access Journals (Sweden)

Xiaobing Kong

2013-01-01

Full Text Available Constituting reliable optimal solution is a key issue for the nonlinear constrained model predictive control. Input-output feedback linearization is a popular method in nonlinear control. By using an input-output feedback linearizing controller, the original linear input constraints will change to nonlinear constraints and sometimes the constraints are state dependent. This paper presents an iterative quadratic program (IQP routine on the continuous-time system. To guarantee its convergence, another iterative approach is incorporated. The proposed algorithm can reach a feasible solution over the entire prediction horizon. Simulation results on both a numerical example and the continuous stirred tank reactors (CSTR demonstrate the effectiveness of the proposed method.

Development and adjustment of programs for solving systems of linear equations

International Nuclear Information System (INIS)

Fujimura, Toichiro

1978-03-01

Programs for solving the systems of linear equations have been adjusted and developed in expanding the scientific subroutine library SSL. The principal programs adjusted are based on the congruent method, method of product form of the inverse, orthogonal method, Crout's method for sparse system, and acceleration of iterative methods. The programs developed are based on the escalator method, direct parallel residue method and block tridiagonal method for band system. Described are usage of the programs developed and their future improvement. FORTRAN lists with simple examples in tests of the programs are also given. (auth.)

Closed-form solutions for linear regulator-design of mechanical systems including optimal weighting matrix selection

Science.gov (United States)

Hanks, Brantley R.; Skelton, Robert E.

1991-01-01

This paper addresses the restriction of Linear Quadratic Regulator (LQR) solutions to the algebraic Riccati Equation to design spaces which can be implemented as passive structural members and/or dampers. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical systems. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist. Some examples of simple spring mass systems are shown to illustrate key points.

Non-linear nuclear engineering models as genetic programming application; Modelos nao-lineares de engenharia nuclear como aplicacao de programacao genetica

Energy Technology Data Exchange (ETDEWEB)

Domingos, Roberto P.; Schirru, Roberto; Martinez, Aquilino S. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia

1997-12-01

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.

Growth and Zeros of Meromorphic Solutions to Second-Order Linear Differential Equations

Directory of Open Access Journals (Sweden)

Maamar Andasmas

2016-04-01

Full Text Available The main purpose of this article is to investigate the growth of meromorphic solutions to homogeneous and non-homogeneous second order linear differential equations f00+Af0+Bf = F, where A(z, B (z and F (z are meromorphic functions with finite order having only finitely many poles. We show that, if there exist a positive constants σ > 0, α > 0 such that |A(z| ≥ eα|z|σ as |z| → +∞, z ∈ H, where dens{|z| : z ∈ H} > 0 and ρ = max{ρ(B, ρ(F} < σ, then every transcendental meromorphic solution f has an infinite order. Further, we give some estimates of their hyper-order, exponent and hyper-exponent of convergence of distinct zeros.

A non-linear programming approach to the computer-aided design of regulators using a linear-quadratic formulation

Science.gov (United States)

Fleming, P.

1985-01-01

A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.

Weak linear degeneracy and lifespan of classical solutions for first order quasilinear hyperbolic systems

International Nuclear Information System (INIS)

Li Tatsien

1994-01-01

By means of the concept of the weak linear degeneracy, one gets the global existence and the sharp estimate of the lifespan of C 1 solutions to the Cauchy problem for general first order quasilinear hyperbolic systems with small initial data with compact support. (author). 23 refs, 1 fig

Stationary solutions of linear stochastic delay differential equations: applications to biological systems.

Science.gov (United States)

Frank, T D; Beek, P J

2001-08-01

Recently, Küchler and Mensch [Stochastics Stochastics Rep. 40, 23 (1992)] derived exact stationary probability densities for linear stochastic delay differential equations. This paper presents an alternative derivation of these solutions by means of the Fokker-Planck approach introduced by Guillouzic [Phys. Rev. E 59, 3970 (1999); 61, 4906 (2000)]. Applications of this approach, which is argued to have greater generality, are discussed in the context of stochastic models for population growth and tracking movements.

Genetic programming over context-free languages with linear constraints for the knapsack problem: first results.

Science.gov (United States)

Bruhn, Peter; Geyer-Schulz, Andreas

2002-01-01

In this paper, we introduce genetic programming over context-free languages with linear constraints for combinatorial optimization, apply this method to several variants of the multidimensional knapsack problem, and discuss its performance relative to Michalewicz's genetic algorithm with penalty functions. With respect to Michalewicz's approach, we demonstrate that genetic programming over context-free languages with linear constraints improves convergence. A final result is that genetic programming over context-free languages with linear constraints is ideally suited to modeling complementarities between items in a knapsack problem: The more complementarities in the problem, the stronger the performance in comparison to its competitors.

q-analogue of summability of formal solutions of some linear q-difference-differential equations

Directory of Open Access Journals (Sweden)

Hidetoshi Tahara

2015-01-01

Full Text Available Let \\(q\\gt 1\\. The paper considers a linear \\(q\\-difference-differential equation: it is a \\(q\\-difference equation in the time variable \\(t\\, and a partial differential equation in the space variable \\(z\\. Under suitable conditions and by using \\(q\\-Borel and \\(q\\-Laplace transforms (introduced by J.-P. Ramis and C. Zhang, the authors show that if it has a formal power series solution \\(\\hat{X}(t,z\\ one can construct an actual holomorphic solution which admits \\(\\hat{X}(t,z\\ as a \\(q\\-Gevrey asymptotic expansion of order \\(1\\.

A LINEAR PROGRAMMING METHOD TO ENHANCE RESOURCE UTILIZATION CASE OF ETHIOPIAN APPAREL SECTOR

Directory of Open Access Journals (Sweden)

Gezahegn Tesfaye

2016-06-01

Full Text Available The Ethiopian industrial development strategy is characterized by export-led and labor intensive industrialization. The country is emerging as the most important investment destination in its apparel sector. Thought this sector is expected to generate more income from the export market, its export earnings remain trivial mainly due to the inefficient organizational resource utilization. One of the competent techniques that help companies to efficiently improve the use of their resources to increase their profit is linear programming. In apparel manufacturing firms, efficient use of materials such as fabrics and sewing threads and processing time at different stages of production as well as minimization of labor and materials cost are necessary to enhance their profitability. Cutting, sewing, and finishing operations deserve more attention for apparel process optimization. However, the issue of proper resource allocation remains an unsolved problem within the Ethiopian apparel industry. The aim of this research is to devise efficient resource utilization mechanism for Ethiopian apparel sector to improve their resource utilization and profitability, taking one of the garment factories engaged in the export market as a case study. Five types of products the company is currently producing, the amount of resources employed to produce each unit of the products, and the value of profit per unit from the sale of each products have been collected from the case company. The monthly availability of resources utilized and the monthly production volume of the five products have also been collected from the company. The data gathered was mathematically modeled using a linear programming technique, and solved using MS-Excel solver. The findings of the study depicts that all of the organizational resources are severely underutilized. This research proved that the resource utilization of the case company can be improved from 46.41% of the current resource

Linear homotopy solution of nonlinear systems of equations in geodesy

Science.gov (United States)

Paláncz, Béla; Awange, Joseph L.; Zaletnyik, Piroska; Lewis, Robert H.

2010-01-01

A fundamental task in geodesy is solving systems of equations. Many geodetic problems are represented as systems of multivariate polynomials. A common problem in solving such systems is improper initial starting values for iterative methods, leading to convergence to solutions with no physical meaning, or to convergence that requires global methods. Though symbolic methods such as Groebner bases or resultants have been shown to be very efficient, i.e., providing solutions for determined systems such as 3-point problem of 3D affine transformation, the symbolic algebra can be very time consuming, even with special Computer Algebra Systems (CAS). This study proposes the Linear Homotopy method that can be implemented easily in high-level computer languages like C++ and Fortran that are faster than CAS by at least two orders of magnitude. Using Mathematica, the power of Homotopy is demonstrated in solving three nonlinear geodetic problems: resection, GPS positioning, and affine transformation. The method enlarging the domain of convergence is found to be efficient, less sensitive to rounding of numbers, and has lower complexity compared to other local methods like Newton-Raphson.

Stochastic linear programming models, theory, and computation

CERN Document Server

Kall, Peter

2011-01-01

This new edition of Stochastic Linear Programming: Models, Theory and Computation has been brought completely up to date, either dealing with or at least referring to new material on models and methods, including DEA with stochastic outputs modeled via constraints on special risk functions (generalizing chance constraints, ICC’s and CVaR constraints), material on Sharpe-ratio, and Asset Liability Management models involving CVaR in a multi-stage setup. To facilitate use as a text, exercises are included throughout the book, and web access is provided to a student version of the authors’ SLP-IOR software. Additionally, the authors have updated the Guide to Available Software, and they have included newer algorithms and modeling systems for SLP. The book is thus suitable as a text for advanced courses in stochastic optimization, and as a reference to the field. From Reviews of the First Edition: "The book presents a comprehensive study of stochastic linear optimization problems and their applications. … T...

A Proposed Method for Solving Fuzzy System of Linear Equations

Directory of Open Access Journals (Sweden)

Reza Kargar

2014-01-01

Full Text Available This paper proposes a new method for solving fuzzy system of linear equations with crisp coefficients matrix and fuzzy or interval right hand side. Some conditions for the existence of a fuzzy or interval solution of m×n linear system are derived and also a practical algorithm is introduced in detail. The method is based on linear programming problem. Finally the applicability of the proposed method is illustrated by some numerical examples.

Fitting program for linear regressions according to Mahon (1996)

Energy Technology Data Exchange (ETDEWEB)

2018-01-09

This program takes the users' Input data and fits a linear regression to it using the prescription presented by Mahon (1996). Compared to the commonly used York fit, this method has the correct prescription for measurement error propagation. This software should facilitate the proper fitting of measurements with a simple Interface.

Analysis of Students' Errors on Linear Programming at Secondary ...

African Journals Online (AJOL)

The purpose of this study was to identify secondary school students' errors on linear programming at 'O' level. It is based on the fact that students' errors inform teaching hence an essential tool for any serious mathematics teacher who intends to improve mathematics teaching. The study was guided by a descriptive survey ...

Life cycle cost optimization of biofuel supply chains under uncertainties based on interval linear programming

DEFF Research Database (Denmark)

Ren, Jingzheng; Dong, Liang; Sun, Lu

2015-01-01

in this model, and the price of the resources, the yield of grain and the market demands were regarded as interval numbers instead of constants. An interval linear programming was developed, and a method for solving interval linear programming was presented. An illustrative case was studied by the proposed...

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.

Fast solution of elliptic partial differential equations using linear combinations of plane waves.

Science.gov (United States)

Pérez-Jordá, José M

2016-02-01

Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations Ax=b, where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O(NlogN) memory and executing an iteration in O(Nlog(2)N) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.

Discounted semi-Markov decision processes : linear programming and policy iteration

NARCIS (Netherlands)

Wessels, J.; van Nunen, J.A.E.E.

1975-01-01

For semi-Markov decision processes with discounted rewards we derive the well known results regarding the structure of optimal strategies (nonrandomized, stationary Markov strategies) and the standard algorithms (linear programming, policy iteration). Our analysis is completely based on a primal

Discounted semi-Markov decision processes : linear programming and policy iteration

NARCIS (Netherlands)

Wessels, J.; van Nunen, J.A.E.E.

1974-01-01

For semi-Markov decision processes with discounted rewards we derive the well known results regarding the structure of optimal strategies (nonrandomized, stationary Markov strategies) and the standard algorithms (linear programming, policy iteration). Our analysis is completely based on a primal

Solution of second order linear fuzzy difference equation by Lagrange's multiplier method

Directory of Open Access Journals (Sweden)

Sankar Prasad Mondal

2016-06-01

Full Text Available In this paper we execute the solution procedure for second order linear fuzzy difference equation by Lagrange's multiplier method. In crisp sense the difference equation are easy to solve, but when we take in fuzzy sense it forms a system of difference equation which is not so easy to solve. By the help of Lagrange's multiplier we can solved it easily. The results are illustrated by two different numerical examples and followed by two applications.

Exact Solution of Mutator Model with Linear Fitness and Finite Genome Length

Science.gov (United States)

Saakian, David B.

2017-08-01

We considered the infinite population version of the mutator phenomenon in evolutionary dynamics, looking at the uni-directional mutations in the mutator-specific genes and linear selection. We solved exactly the model for the finite genome length case, looking at the quasispecies version of the phenomenon. We calculated the mutator probability both in the statics and dynamics. The exact solution is important for us because the mutator probability depends on the genome length in a highly non-trivial way.

A multiple objective mixed integer linear programming model for power generation expansion planning

Energy Technology Data Exchange (ETDEWEB)

Antunes, C. Henggeler; Martins, A. Gomes [INESC-Coimbra, Coimbra (Portugal); Universidade de Coimbra, Dept. de Engenharia Electrotecnica, Coimbra (Portugal); Brito, Isabel Sofia [Instituto Politecnico de Beja, Escola Superior de Tecnologia e Gestao, Beja (Portugal)

2004-03-01

Power generation expansion planning inherently involves multiple, conflicting and incommensurate objectives. Therefore, mathematical models become more realistic if distinct evaluation aspects, such as cost and environmental concerns, are explicitly considered as objective functions rather than being encompassed by a single economic indicator. With the aid of multiple objective models, decision makers may grasp the conflicting nature and the trade-offs among the different objectives in order to select satisfactory compromise solutions. This paper presents a multiple objective mixed integer linear programming model for power generation expansion planning that allows the consideration of modular expansion capacity values of supply-side options. This characteristic of the model avoids the well-known problem associated with continuous capacity values that usually have to be discretized in a post-processing phase without feedback on the nature and importance of the changes in the attributes of the obtained solutions. Demand-side management (DSM) is also considered an option in the planning process, assuming there is a sufficiently large portion of the market under franchise conditions. As DSM full costs are accounted in the model, including lost revenues, it is possible to perform an evaluation of the rate impact in order to further inform the decision process (Author)

BEAMPATH: a program library for beam dynamics simulation in linear accelerators

International Nuclear Information System (INIS)

Batygin, Y.K.

1992-01-01

A structured programming technique was used to develop software for space charge dominated beams investigation in linear accelerators. The method includes hierarchical program design using program independent modules and a flexible combination of modules to provide a most effective version of structure for every specific case of simulation. A modular program BEAMPATH was developed for 2D and 3D particle-in-cell simulation of beam dynamics in a structure containing RF gaps, radio-frequency quadrupoles (RFQ), multipole lenses, waveguides, bending magnets and solenoids. (author) 5 refs.; 2 figs

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.

Analytical SN solutions in heterogeneous slabs using symbolic algebra computer programs

International Nuclear Information System (INIS)

Warsa, J.S.

2002-01-01

A modern symbolic algebra computer program, MAPLE, is used to compute solutions to the well-known analytical discrete ordinates, or S N , solutions in one-dimensional, slab geometry. Symbolic algebra programs compute the solutions with arbitrary precision and are free of spatial discretization error so they can be used to investigate new discretizations for one-dimensional slab, geometry S N methods. Pointwise scalar flux solutions are computed for several sample calculations of interest. Sample MAPLE command scripts are provided to illustrate how easily the theory can be translated into a working solution and serve as a complete tool capable of computing analytical S N solutions for mono-energetic, one-dimensional transport problems

A Linear Programming Approach to Complex Games: An Application to Nuclear Exchange Models

National Research Council Canada - National Science Library

Oelrich, I

2002-01-01

.... Like the MESA model, the exchange is cast in terms of game theory, using linear approximations and an optimal allocation defined by a user-specified objective function Solutions are better using...

Relaxation Methods for Strictly Convex Regularizations of Piecewise Linear Programs

International Nuclear Information System (INIS)

Kiwiel, K. C.

1998-01-01

We give an algorithm for minimizing the sum of a strictly convex function and a convex piecewise linear function. It extends several dual coordinate ascent methods for large-scale linearly constrained problems that occur in entropy maximization, quadratic programming, and network flows. In particular, it may solve exact penalty versions of such (possibly inconsistent) problems, and subproblems of bundle methods for nondifferentiable optimization. It is simple, can exploit sparsity, and in certain cases is highly parallelizable. Its global convergence is established in the recent framework of B -functions (generalized Bregman functions)

A Partitioning and Bounded Variable Algorithm for Linear Programming

Science.gov (United States)

Sheskin, Theodore J.

2006-01-01

An interesting new partitioning and bounded variable algorithm (PBVA) is proposed for solving linear programming problems. The PBVA is a variant of the simplex algorithm which uses a modified form of the simplex method followed by the dual simplex method for bounded variables. In contrast to the two-phase method and the big M method, the PBVA does…

Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization.

Science.gov (United States)

Simpson, Matthew J

2015-01-01

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0exact solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i) the rate at which the domain elongates, (ii) the diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).

A Lie-admissible method of integration of Fokker-Planck equations with non-linear coefficients (exact and numerical solutions)

International Nuclear Information System (INIS)

Fronteau, J.; Combis, P.

1984-08-01

A Lagrangian method is introduced for the integration of non-linear Fokker-Planck equations. Examples of exact solutions obtained in this way are given, and also the explicit scheme used for the computation of numerical solutions. The method is, in addition, shown to be of a Lie-admissible type

On the existence of tunneling bounce solutions in piecewise linear potentials

International Nuclear Information System (INIS)

Dutta, Koushik; Hector, Cecelie; Konstandin, Thomas; Vaudrevange, Pascal M.; Westphal, Alexander

2012-02-01

Coleman tunneling in a general scalar potential with two non-degenerate minima is known to have an approximation in terms of a piecewise linear triangular-shaped potential with sharp 'kinks' at the place of the local minima. This approximate potential has a regime where the existence of the bounce solution needs the scalar field to 'wait' for some amount of Euclidean time at one of the 'kinks'. We discuss under which circumstances the correct bounce action can be consistently obtained as the limiting case of a regular scalar potential where 'kinks' are resolved as locally smooth 'cap' regions. (orig.)

Optimal traffic control in highway transportation networks using linear programming

KAUST Repository

Li, Yanning; Canepa, Edward S.; Claudel, Christian G.

2014-01-01

of the Hamilton-Jacobi PDE, the problem of controlling the state of the system on a network link in a finite horizon can be posed as a Linear Program. Assuming all intersections in the network are controllable, we show that the optimization approach can

Mathematical solution of multilevel fractional programming problem with fuzzy goal programming approach

Science.gov (United States)

Lachhwani, Kailash; Poonia, Mahaveer Prasad

2012-08-01

In this paper, we show a procedure for solving multilevel fractional programming problems in a large hierarchical decentralized organization using fuzzy goal programming approach. In the proposed method, the tolerance membership functions for the fuzzily described numerator and denominator part of the objective functions of all levels as well as the control vectors of the higher level decision makers are respectively defined by determining individual optimal solutions of each of the level decision makers. A possible relaxation of the higher level decision is considered for avoiding decision deadlock due to the conflicting nature of objective functions. Then, fuzzy goal programming approach is used for achieving the highest degree of each of the membership goal by minimizing negative deviational variables. We also provide sensitivity analysis with variation of tolerance values on decision vectors to show how the solution is sensitive to the change of tolerance values with the help of a numerical example.

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.

Optimization of the annual construction program solutions

Directory of Open Access Journals (Sweden)

Oleinik Pavel

2017-01-01

Full Text Available The article considers potentially possible optimization solutions in scheduling while forming the annual production programs of the construction complex organizations. The optimization instrument is represented as a two-component system. As a fundamentally new approach in the first block of the annual program solutions, the authors propose to use a scientifically grounded methodology for determining the scope of work permissible for the transfer to a subcontractor without risk of General Contractor’s management control losing over the construction site. For this purpose, a special indicator is introduced that characterizes the activity of the general construction organization - the coefficient of construction production management. In the second block, the principal methods for the formation of calendar plans for the fulfillment of the critical work effort by the leading stream are proposed, depending on the intensity characteristic.

Nutrient density score of typical Indonesian foods and dietary formulation using linear programming.

Science.gov (United States)

Jati, Ignasius Radix A P; Vadivel, Vellingiri; Nöhr, Donatus; Biesalski, Hans Konrad

2012-12-01

The present research aimed to analyse the nutrient density (ND), nutrient adequacy score (NAS) and energy density (ED) of Indonesian foods and to formulate a balanced diet using linear programming. Data on typical Indonesian diets were obtained from the Indonesian Socio-Economic Survey 2008. ND was investigated for 122 Indonesian foods. NAS was calculated for single nutrients such as Fe, Zn and vitamin A. Correlation analysis was performed between ND and ED, as well as between monthly expenditure class and food consumption pattern in Indonesia. Linear programming calculations were performed using the software POM-QM for Windows version 3. Republic of Indonesia, 2008. Public households (n 68 800). Vegetables had the highest ND of the food groups, followed by animal-based foods, fruits and staple foods. Based on NAS, the top ten food items for each food group were identified. Most of the staple foods had high ED and contributed towards daily energy fulfillment, followed by animal-based foods, vegetables and fruits. Commodities with high ND tended to have low ED. Linear programming could be used to formulate a balanced diet. In contrast to staple foods, purchases of fruit, vegetables and animal-based foods increased with the rise of monthly expenditure. People should select food items based on ND and NAS to alleviate micronutrient deficiencies in Indonesia. Dietary formulation calculated using linear programming to achieve RDA levels for micronutrients could be recommended for different age groups of the Indonesian population.

The structure of solutions of the matrix linear unilateral polynomial equation with two variables

Directory of Open Access Journals (Sweden)

N. S. Dzhaliuk

2017-07-01

Full Text Available We investigate the structure of solutions of the matrix linear polynomial equation $A(\\lambdaX(\\lambda+B(\\lambdaY(\\lambda=C(\\lambda,$ in particular, possible degrees of the solutions. The solving of this equation is reduced to the solving of the equivalent matrix polynomial equation with matrix coefficients in triangular forms with invariant factors on the main diagonals, to which the matrices $A (\\lambda, B(\\lambda$ \\ and \\ $C(\\lambda$ are reduced by means of semiscalar equivalent transformations. On the basis of it, we have pointed out the bounds of the degrees of the matrix polynomial equation solutions. Necessary and sufficient conditions for the uniqueness of a solution with a minimal degree are established. An effective method for constructing minimal degree solutions of the equations is suggested. In this article, unlike well-known results about the estimations of the degrees of the solutions of the matrix polynomial equations in which both matrix coefficients are regular or at least one of them is regular, we have considered the case when the matrix polynomial equation has arbitrary matrix coefficients $A(\\lambda$ and $B(\\lambda.$ 

Dual solutions of three-dimensional flow and heat transfer over a non-linearly stretching/shrinking sheet

Science.gov (United States)

Naganthran, Kohilavani; Nazar, Roslinda; Pop, Ioan

2018-05-01

This study investigated the influence of the non-linearly stretching/shrinking sheet on the boundary layer flow and heat transfer. A proper similarity transformation simplified the system of partial differential equations into a system of ordinary differential equations. This system of similarity equations is then solved numerically by using the bvp4c function in the MATLAB software. The generated numerical results presented graphically and discussed in the relevance of the governing parameters. Dual solutions found as the sheet stretched and shrunk in the horizontal direction. Stability analysis showed that the first solution is physically realizable whereas the second solution is not practicable.

Solutions manual to accompany finite mathematics models and applications

CERN Document Server

Morris, Carla C

2015-01-01

A solutions manual to accompany Finite Mathematics: Models and Applications In order to emphasize the main concepts of each chapter, Finite Mathematics: Models and Applications features plentiful pedagogical elements throughout such as special exercises, end notes, hints, select solutions, biographies of key mathematicians, boxed key principles, a glossary of important terms and topics, and an overview of use of technology. The book encourages the modeling of linear programs and their solutions and uses common computer software programs such as LINDO. In addition to extensive chapters on pr

Decision-making methodology of optimal shielding materials by using fuzzy linear programming

International Nuclear Information System (INIS)

Kanai, Y.; Miura, T.; Hirao, Y.

2000-01-01

The main purpose of our studies are to select materials and determine the ratio of constituent materials as the first stage of optimum shielding design to suit the individual requirements of nuclear reactors, reprocessing facilities, casks for shipping spent fuel, etc. The parameters of the shield optimization are cost, space, weight and some shielding properties such as activation rates or individual irradiation and cooling time, and total dose rate for neutrons (including secondary gamma ray) and for primary gamma ray. Using conventional two-valued logic (i.e. crisp) approaches, huge combination calculations are needed to identify suitable materials for optimum shielding design. Also, re-computation is required for minor changes, as the approach does not react sensitively to the computation result. Present approach using a fuzzy linear programming method is much of the decision-making toward the satisfying solution might take place in fuzzy environment. And it can quickly and easily provide a guiding principle of optimal selection of shielding materials under the above-mentioned conditions. The possibility or reducing radiation effects by optimizing the ratio of constituent materials is investigated. (author)

New conformations of linear polyubiquitin chains from crystallographic and solution-scattering studies expand the conformational space of polyubiquitin.

Science.gov (United States)

Thach, Trung Thanh; Shin, Donghyuk; Han, Seungsu; Lee, Sangho

2016-04-01

The conformational flexibility of linkage-specific polyubiquitin chains enables ubiquitylated proteins and their receptors to be involved in a variety of cellular processes. Linear or Met1-linked polyubiquitin chains, associated with nondegradational cellular signalling pathways, have been known to adopt multiple conformations from compact to extended conformations. However, the extent of such conformational flexibility remains open. Here, the crystal structure of linear Ub2 was determined in a more compact conformation than that of the previously known structure (PDB entry 3axc). The two structures differ significantly from each other, as shown by an r.m.s.d. between C(α) atoms of 3.1 Å. The compactness of the linear Ub2 structure in comparison with PDB entry 3axc is supported by smaller values of the radius of gyration (Rg; 18 versus 18.9 Å) and the maximum interatomic distance (Dmax; 55.5 versus 57.8 Å). Extra intramolecular hydrogen bonds formed among polar residues between the distal and proximal ubiquitin moieties seem to contribute to stabilization of the compact conformation of linear Ub2. An ensemble of three semi-extended and extended conformations of linear Ub2 was also observed by small-angle X-ray scattering (SAXS) analysis in solution. In addition, the conformational heterogeneity in linear polyubiquitin chains is clearly manifested by SAXS analyses of linear Ub3 and Ub4: at least three distinct solution conformations are observed in each chain, with the linear Ub3 conformations being compact. The results expand the extent of conformational space of linear polyubiquitin chains and suggest that changes in the conformational ensemble may be pivotal in mediating multiple signalling pathways.

Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues.

Science.gov (United States)

Kumar, Dinesh; Kumar, P; Rai, K N

2017-11-01

This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to predict more accurate results. A numerical method of line which is based on finite difference and Runge-Kutta (4,5) schemes, is used to solve the present non-linear problem. Under specific case, the exact solution has been obtained and compared with the present numerical scheme, and we found that those are in good agreement. A comparison based on model selection criterion (AIC) has been made among non-linear DPL models when the variation of blood perfusion rate with temperature is of constant, linear and exponential type with the experimental data and it has been found that non-linear DPL model with exponential variation of blood perfusion rate is closest to the experimental data. In addition, it is found that due to absence of phase-lag phenomena in Pennes bioheat transfer model, it achieves steady state more quickly and always predict higher temperature than thermal and DPL non-linear models. The effect of coefficient of blood perfusion rate, dimensionless heating frequency and Kirchoff number on dimensionless temperature distribution has also been analyzed. The whole analysis is presented in dimensionless form. Copyright © 2017 Elsevier Inc. All rights reserved.

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.

Fast decay of solutions for linear wave equations with dissipation localized near infinity in an exterior domain

Science.gov (United States)

Ryo, Ikehata

Uniform energy and L2 decay of solutions for linear wave equations with localized dissipation will be given. In order to derive the L2-decay property of the solution, a useful device whose idea comes from Ikehata-Matsuyama (Sci. Math. Japon. 55 (2002) 33) is used. In fact, we shall show that the L2-norm and the total energy of solutions, respectively, decay like O(1/ t) and O(1/ t2) as t→+∞ for a kind of the weighted initial data.

A mixed integer linear program for an integrated fishery | Hasan ...

African Journals Online (AJOL)

... and labour allocation of quota based integrated fisheries. We demonstrate the workability of our model with a numerical example and sensitivity analysis based on data obtained from one of the major fisheries in New Zealand. Keywords: mixed integer linear program, fishing, trawler scheduling, processing, quotas ORiON: ...

Timber management planning with timber ram and goal programming

Science.gov (United States)

Richard C. Field

1978-01-01

By using goal programming to enhance the linear programming of Timber RAM, multiple decision criteria were incorporated in the timber management planning of a National Forest in the southeastern United States. Combining linear and goal programming capitalizes on the advantages of the two techniques and produces operationally feasible solutions. This enhancement may...

A linear programming approach for placement of applicants to academic programs.

Science.gov (United States)

Kassa, Biniyam Asmare

2013-01-01

This paper reports a linear programming approach for placement of applicants to study programs developed and implemented at the college of Business & Economics, Bahir Dar University, Bahir Dar, Ethiopia. The approach is estimated to significantly streamline the placement decision process at the college by reducing required man hour as well as the time it takes to announce placement decisions. Compared to the previous manual system where only one or two placement criteria were considered, the new approach allows the college's management to easily incorporate additional placement criteria, if needed. Comparison of our approach against manually constructed placement decisions based on actual data for the 2012/13 academic year suggested that about 93 percent of the placements from our model concur with the actual placement decisions. For the remaining 7 percent of placements, however, the actual placements made by the manual system display inconsistencies of decisions judged against the very criteria intended to guide placement decisions by the college's program management office. Overall, the new approach proves to be a significant improvement over the manual system in terms of efficiency of the placement process and the quality of placement decisions.

An algorithm for computing the hull of the solution set of interval linear equations

Czech Academy of Sciences Publication Activity Database

Rohn, Jiří

2011-01-01

Roč. 435, č. 2 (2011), s. 193-201 ISSN 0024-3795 R&D Projects: GA ČR GA201/09/1957; GA ČR GC201/08/J020 Institutional research plan: CEZ:AV0Z10300504 Keywords : interval linear equations * solution set * interval hull * algorithm * absolute value inequality Subject RIV: BA - General Mathematics Impact factor: 0.974, year: 2011

On the existence of tunneling bounce solutions in piecewise linear potentials

Energy Technology Data Exchange (ETDEWEB)

Dutta, Koushik; Hector, Cecelie; Konstandin, Thomas; Vaudrevange, Pascal M.; Westphal, Alexander

2012-02-15

Coleman tunneling in a general scalar potential with two non-degenerate minima is known to have an approximation in terms of a piecewise linear triangular-shaped potential with sharp 'kinks' at the place of the local minima. This approximate potential has a regime where the existence of the bounce solution needs the scalar field to 'wait' for some amount of Euclidean time at one of the 'kinks'. We discuss under which circumstances the correct bounce action can be consistently obtained as the limiting case of a regular scalar potential where 'kinks' are resolved as locally smooth 'cap' regions. (orig.)

Solution of Large Systems of Linear Equations with Quadratic or Non-Quadratic Matrices and Deconvoiution of Spectra

Energy Technology Data Exchange (ETDEWEB)

Nygaard, K

1967-12-15

The numerical deconvolution of spectra is equivalent to the solution of a (large) system of linear equations with a matrix which is not necessarily a square matrix. The demand that the square sum of the residual errors shall be minimum is not in general sufficient to ensure a unique or 'sound' solution. Therefore other demands which may include the demand for minimum square errors are introduced which lead to 'sound' and 'non-oscillatory' solutions irrespective of the shape of the original matrix and of the determinant of the matrix of the normal equations.

Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization.

Directory of Open Access Journals (Sweden)

Matthew J Simpson

Full Text Available Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i the rate at which the domain elongates, (ii the diffusivity associated with the spreading density profile, (iii the reaction rate, and (iv the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t.

Designing Camera Networks by Convex Quadratic Programming

KAUST Repository

Ghanem, Bernard; Wonka, Peter; Cao, Yuanhao

2015-01-01

be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution

ITMETH, Iterative Routines for Linear System

International Nuclear Information System (INIS)

Greenbaum, A.

1989-01-01

1 - Description of program or function: ITMETH is a collection of iterative routines for solving large, sparse linear systems. 2 - Method of solution: ITMETH solves general linear systems of the form AX=B using a variety of methods: Jacobi iteration; Gauss-Seidel iteration; incomplete LU decomposition or matrix splitting with iterative refinement; diagonal scaling, matrix splitting, or incomplete LU decomposition with the conjugate gradient method for the problem AA'Y=B, X=A'Y; bi-conjugate gradient method with diagonal scaling, matrix splitting, or incomplete LU decomposition; and ortho-min method with diagonal scaling, matrix splitting, or incomplete LU decomposition. ITMETH also solves symmetric positive definite linear systems AX=B using the conjugate gradient method with diagonal scaling or matrix splitting, or the incomplete Cholesky conjugate gradient method

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.

User's Guide to the Weighted-Multiple-Linear Regression Program (WREG version 1.0)

Science.gov (United States)

Eng, Ken; Chen, Yin-Yu; Kiang, Julie.E.

2009-01-01

Streamflow is not measured at every location in a stream network. Yet hydrologists, State and local agencies, and the general public still seek to know streamflow characteristics, such as mean annual flow or flood flows with different exceedance probabilities, at ungaged basins. The goals of this guide are to introduce and familiarize the user with the weighted multiple-linear regression (WREG) program, and to also provide the theoretical background for program features. The program is intended to be used to develop a regional estimation equation for streamflow characteristics that can be applied at an ungaged basin, or to improve the corresponding estimate at continuous-record streamflow gages with short records. The regional estimation equation results from a multiple-linear regression that relates the observable basin characteristics, such as drainage area, to streamflow characteristics.

Solution of the linearly anisotropic neutron transport problem in a infinite cylinder combining the decomposition and HTSN methods

International Nuclear Information System (INIS)

Goncalves, Glenio A.; Bodmann, Bardo; Bogado, Sergio; Vilhena, Marco T.

2008-01-01

Analytical solutions for neutron transport in cylindrical geometry is available for isotropic problems, but to the best of our knowledge for anisotropic problems are not available, yet. In this work, an analytical solution for the neutron transport equation in an infinite cylinder assuming anisotropic scattering is reported. Here we specialize the solution, without loss of generality, for the linearly anisotropic problem using the combined decomposition and HTS N methods. The key feature of this method consists in the application of the decomposition method to the anisotropic problem by virtue of the fact that the inverse of the operator associated to isotropic problem is well know and determined by the HTS N approach. So far, following the idea of the decomposition method, we apply this operator to the integral term, assuming that the angular flux appearing in the integrand is considered to be equal to the HTS N solution interpolated by polynomial considering only even powers. This leads to the first approximation for an anisotropic solution. Proceeding further, we replace this solution for the angular flux in the integral and apply again the inverse operator for the isotropic problem in the integral term and obtain a new approximation for the angular flux. This iterative procedure yields a closed form solution for the angular flux. This methodology can be generalized, in a straightforward manner, for transport problems with any degree of anisotropy. For the sake of illustration, we report numerical simulations for linearly anisotropic transport problems. (author)

A Comparison of Linear and Systems Thinking Approaches for Program Evaluation Illustrated Using the Indiana Interdisciplinary GK-12

Science.gov (United States)

Dyehouse, Melissa; Bennett, Deborah; Harbor, Jon; Childress, Amy; Dark, Melissa

2009-01-01

Logic models are based on linear relationships between program resources, activities, and outcomes, and have been used widely to support both program development and evaluation. While useful in describing some programs, the linear nature of the logic model makes it difficult to capture the complex relationships within larger, multifaceted…

Optimal Control of Switching Linear Systems

Directory of Open Access Journals (Sweden)

Ali Benmerzouga

2004-06-01

Full Text Available A solution to the control of switching linear systems with input constraints was given in Benmerzouga (1997 for both the conventional enumeration approach and the new approach. The solution given there turned out to be not unique. The main objective in this work is to determine the optimal control sequences {Ui(k ,  i = 1,..., M ;  k = 0, 1, ...,  N -1} which transfer the system from a given initial state  X0  to a specific target state  XT  (or to be as close as possible by using the same discrete time solution obtained in Benmerzouga (1997 and minimizing a running cost-to-go function. By using the dynamic programming technique, the optimal solution is found for both approaches given in Benmerzouga (1997. The computational complexity of the modified algorithm is also given.

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...

On the boundedness and integration of non-oscillatory solutions of certain linear differential equations of second order.

Science.gov (United States)

Tunç, Cemil; Tunç, Osman

2016-01-01

In this paper, certain system of linear homogeneous differential equations of second-order is considered. By using integral inequalities, some new criteria for bounded and [Formula: see text]-solutions, upper bounds for values of improper integrals of the solutions and their derivatives are established to the considered system. The obtained results in this paper are considered as extension to the results obtained by Kroopnick (2014) [1]. An example is given to illustrate the obtained results.

An efficient linear approach in the reservoirs operation for electric power generation; Uma eficiente abordagem linear na operacao de reservatorios para geracao de energia eletrica

Energy Technology Data Exchange (ETDEWEB)

Zambon, Katia Livia

1997-07-01

A new approach for the Scheduling of Hydrothermal Systems, with a formulation that allows the solution of the problem through the linear programming techniques, otherwise the original form, which is complex and difficult is presented. The models were developed through a linear form for the generation function of hydroelectric plants, successive of the linearization of the cost function of the problem. The linear techniques used were the Simplex Method, with some modification that is is efficient, fast and simple. The important physical aspects of the system were preserved, like the individual representation of the hydroelectric plant, the features of cost function with the exponential increase and the head effect. Besides, this formulation can lead to stochastic approaches. All the optimization methods were implemented for the solution of the problem. The performance obtained were compared with each other and with that obtained through the non linear techniques. The algorithms showed to be efficient, with good results and very near to the optimal behavior of the reservoir operation planning obtained by traditional methods. (author)

A non-linear optimal Discontinuous Petrov-Galerkin method for stabilising the solution of the transport equation

International Nuclear Information System (INIS)

Merton, S. R.; Smedley-Stevenson, R. P.; Pain, C. C.; Buchan, A. G.; Eaton, M. D.

2009-01-01

This paper describes a new Non-Linear Discontinuous Petrov-Galerkin (NDPG) method and application to the one-speed Boltzmann Transport Equation (BTE) for space-time problems. The purpose of the method is to remove unwanted oscillations in the transport solution which occur in the vicinity of sharp flux gradients, while improving computational efficiency and numerical accuracy. This is achieved by applying artificial dissipation in the solution gradient direction, internal to an element using a novel finite element (FE) Riemann approach. The amount of dissipation added acts internal to each element. This is done using a gradient-informed scaling of the advection velocities in the stabilisation term. This makes the method in its most general form non-linear. The method is designed to be independent of angular expansion framework. This is demonstrated for the both discrete ordinates (S N ) and spherical harmonics (P N ) descriptions of the angular variable. Results show the scheme performs consistently well in demanding time dependent and multi-dimensional radiation transport problems. (authors)

A risk explicit interval linear programming model for uncertainty-based environmental economic optimization in the Lake Fuxian watershed, China.

Science.gov (United States)

Zhang, Xiaoling; Huang, Kai; Zou, Rui; Liu, Yong; Yu, Yajuan

2013-01-01

The conflict of water environment protection and economic development has brought severe water pollution and restricted the sustainable development in the watershed. A risk explicit interval linear programming (REILP) method was used to solve integrated watershed environmental-economic optimization problem. Interval linear programming (ILP) and REILP models for uncertainty-based environmental economic optimization at the watershed scale were developed for the management of Lake Fuxian watershed, China. Scenario analysis was introduced into model solution process to ensure the practicality and operability of optimization schemes. Decision makers' preferences for risk levels can be expressed through inputting different discrete aspiration level values into the REILP model in three periods under two scenarios. Through balancing the optimal system returns and corresponding system risks, decision makers can develop an efficient industrial restructuring scheme based directly on the window of "low risk and high return efficiency" in the trade-off curve. The representative schemes at the turning points of two scenarios were interpreted and compared to identify a preferable planning alternative, which has the relatively low risks and nearly maximum benefits. This study provides new insights and proposes a tool, which was REILP, for decision makers to develop an effectively environmental economic optimization scheme in integrated watershed management.

A Risk Explicit Interval Linear Programming Model for Uncertainty-Based Environmental Economic Optimization in the Lake Fuxian Watershed, China

Directory of Open Access Journals (Sweden)

Xiaoling Zhang

2013-01-01

Full Text Available The conflict of water environment protection and economic development has brought severe water pollution and restricted the sustainable development in the watershed. A risk explicit interval linear programming (REILP method was used to solve integrated watershed environmental-economic optimization problem. Interval linear programming (ILP and REILP models for uncertainty-based environmental economic optimization at the watershed scale were developed for the management of Lake Fuxian watershed, China. Scenario analysis was introduced into model solution process to ensure the practicality and operability of optimization schemes. Decision makers’ preferences for risk levels can be expressed through inputting different discrete aspiration level values into the REILP model in three periods under two scenarios. Through balancing the optimal system returns and corresponding system risks, decision makers can develop an efficient industrial restructuring scheme based directly on the window of “low risk and high return efficiency” in the trade-off curve. The representative schemes at the turning points of two scenarios were interpreted and compared to identify a preferable planning alternative, which has the relatively low risks and nearly maximum benefits. This study provides new insights and proposes a tool, which was REILP, for decision makers to develop an effectively environmental economic optimization scheme in integrated watershed management.

Role of statistical linearization in the solution of nonlinear stochastic equations

International Nuclear Information System (INIS)

Budgor, A.B.

1977-01-01

The solution of a generalized Langevin equation is referred to as a stochastic process. If the external forcing function is Gaussian white noise, the forward Kolmogarov equation yields the transition probability density function. Nonlinear problems must be handled by approximation procedures e.g., perturbation theories, eigenfunction expansions, and nonlinear optimization procedures. After some comments on the first two of these, attention is directed to the third, and the method of statistical linearization is used to demonstrate a relation to the former two. Nonlinear stochastic systems exhibiting sustained or forced oscillations and the centered nonlinear Schroedinger equation in the presence of Gaussian white noise excitation are considered as examples. 5 figures, 2 tables

Spillways Scheduling for Flood Control of Three Gorges Reservoir Using Mixed Integer Linear Programming Model

Directory of Open Access Journals (Sweden)

Maoyuan Feng

2014-01-01

Full Text Available This study proposes a mixed integer linear programming (MILP model to optimize the spillways scheduling for reservoir flood control. Unlike the conventional reservoir operation model, the proposed MILP model specifies the spillways status (including the number of spillways to be open and the degree of the spillway opened instead of reservoir release, since the release is actually controlled by using the spillway. The piecewise linear approximation is used to formulate the relationship between the reservoir storage and water release for a spillway, which should be open/closed with a status depicted by a binary variable. The control order and symmetry rules of spillways are described and incorporated into the constraints for meeting the practical demand. Thus, a MILP model is set up to minimize the maximum reservoir storage. The General Algebraic Modeling System (GAMS and IBM ILOG CPLEX Optimization Studio (CPLEX software are used to find the optimal solution for the proposed MILP model. The China’s Three Gorges Reservoir, whose spillways are of five types with the total number of 80, is selected as the case study. It is shown that the proposed model decreases the flood risk compared with the conventional operation and makes the operation more practical by specifying the spillways status directly.

Sixth SIAM conference on applied linear algebra: Final program and abstracts. Final technical report

Energy Technology Data Exchange (ETDEWEB)

NONE

1997-12-31

Linear algebra plays a central role in mathematics and applications. The analysis and solution of problems from an amazingly wide variety of disciplines depend on the theory and computational techniques of linear algebra. In turn, the diversity of disciplines depending on linear algebra also serves to focus and shape its development. Some problems have special properties (numerical, structural) that can be exploited. Some are simply so large that conventional approaches are impractical. New computer architectures motivate new algorithms, and fresh ways to look at old ones. The pervasive nature of linear algebra in analyzing and solving problems means that people from a wide spectrum--universities, industrial and government laboratories, financial institutions, and many others--share an interest in current developments in linear algebra. This conference aims to bring them together for their mutual benefit. Abstracts of papers presented are included.

A linear programming model of diet choice of free-living beavers

NARCIS (Netherlands)

Nolet, BA; VanderVeer, PJ; Evers, EGJ; Ottenheim, MM

1995-01-01

Linear programming has been remarkably successful in predicting the diet choice of generalist herbivores. We used this technique to test the diet choice of free-living beavers (Castor fiber) in the Biesbosch (The Netherlands) under different Foraging goals, i.e. maximization of intake of energy,

Comparison of different methods for the solution of sets of linear equations

International Nuclear Information System (INIS)

Bilfinger, T.; Schmidt, F.

1978-06-01

The application of the conjugate-gradient methods as novel general iterative methods for the solution of sets of linear equations with symmetrical systems matrices led to this paper, where a comparison of these methods with the conventional differently accelerated Gauss-Seidel iteration was carried out. In additon, the direct Cholesky method was also included in the comparison. The studies referred mainly to memory requirement, computing time, speed of convergence, and accuracy of different conditions of the systems matrices, by which also the sensibility of the methods with respect to the influence of truncation errors may be recognized. (orig.) 891 RW [de

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.

SIGMA1-2007, Doppler Broadening ENDF Format Linear-Linear. Interpolated Point Cross Section

International Nuclear Information System (INIS)