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Author: Ralph John Waterman Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
This study evaluates and compares the production use of three nonlinear programming codes. The three codes and their developers are: SUMT by W.C. Mylander, R.L. Holmes and G.P. McCormick, GRG by L.S. Lasdon, A.D. Waren, M.W. Ratner and A. Jain, and GRAVES by G.W. Graves. This is the first computer comparison of these three particular codes. Each code was evaluated with respect to the time and sophistication required of the user and the degree of mandatory or potential interaction between the code and the analyst. The comparison criteria were accuracy, robustness, efficiency and ease of utilization. Eight current and realistic test problems employing from 9-100 variables and 2-20 constraints were used. The results revealed that no single code was superior or inferior in all aspects. The choice of an optimal code among these three would be dependent upon the problems to be solved, the ability of the analyst and the desire of the analyst to alter the code for his own purposes. (Author).
Author: Ralph John Waterman Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
This study evaluates and compares the production use of three nonlinear programming codes. The three codes and their developers are: SUMT by W.C. Mylander, R.L. Holmes and G.P. McCormick, GRG by L.S. Lasdon, A.D. Waren, M.W. Ratner and A. Jain, and GRAVES by G.W. Graves. This is the first computer comparison of these three particular codes. Each code was evaluated with respect to the time and sophistication required of the user and the degree of mandatory or potential interaction between the code and the analyst. The comparison criteria were accuracy, robustness, efficiency and ease of utilization. Eight current and realistic test problems employing from 9-100 variables and 2-20 constraints were used. The results revealed that no single code was superior or inferior in all aspects. The choice of an optimal code among these three would be dependent upon the problems to be solved, the ability of the analyst and the desire of the analyst to alter the code for his own purposes. (Author).
Author: Mokhtar S. Bazaraa Publisher: John Wiley & Sons ISBN: 1118626303 Category : Mathematics Languages : en Pages : 818
Book Description
COMPREHENSIVE COVERAGE OF NONLINEAR PROGRAMMING THEORY AND ALGORITHMS, THOROUGHLY REVISED AND EXPANDED Nonlinear Programming: Theory and Algorithms—now in an extensively updated Third Edition—addresses the problem of optimizing an objective function in the presence of equality and inequality constraints. Many realistic problems cannot be adequately represented as a linear program owing to the nature of the nonlinearity of the objective function and/or the nonlinearity of any constraints. The Third Edition begins with a general introduction to nonlinear programming with illustrative examples and guidelines for model construction. Concentration on the three major parts of nonlinear programming is provided: Convex analysis with discussion of topological properties of convex sets, separation and support of convex sets, polyhedral sets, extreme points and extreme directions of polyhedral sets, and linear programming Optimality conditions and duality with coverage of the nature, interpretation, and value of the classical Fritz John (FJ) and the Karush-Kuhn-Tucker (KKT) optimality conditions; the interrelationships between various proposed constraint qualifications; and Lagrangian duality and saddle point optimality conditions Algorithms and their convergence, with a presentation of algorithms for solving both unconstrained and constrained nonlinear programming problems Important features of the Third Edition include: New topics such as second interior point methods, nonconvex optimization, nondifferentiable optimization, and more Updated discussion and new applications in each chapter Detailed numerical examples and graphical illustrations Essential coverage of modeling and formulating nonlinear programs Simple numerical problems Advanced theoretical exercises The book is a solid reference for professionals as well as a useful text for students in the fields of operations research, management science, industrial engineering, applied mathematics, and also in engineering disciplines that deal with analytical optimization techniques. The logical and self-contained format uniquely covers nonlinear programming techniques with a great depth of information and an abundance of valuable examples and illustrations that showcase the most current advances in nonlinear problems.
Author: Olvi L. Mangasarian Publisher: Academic Press ISBN: 1483260321 Category : Mathematics Languages : en Pages : 486
Book Description
Nonlinear Programming 3 covers the proceedings of the Special Interest Group on Mathematical Programming Symposium conducted by the Computer Sciences Department at the University of Wisconsin, Madison, on July 11-13, 1977. This book is composed of 17 chapters. The first eight chapters describe some of the most effective methods available for solving linearly and nonlinearly constrained optimization problems. The subsequent chapter gives algorithms for the solution of nonlinear equations together with computational experience. Other chapters provide some applications of optimization in operations research and a measurement procedure for optimization algorithm efficiency. These topics are followed by discussion of the methods for solving large quadratic programs and algorithms for solving stationary and fixed point problems. The last chapters consider the minimization of certain types of nondifferentiable functions and a type of Newton method. This book will prove useful to mathematicians and computer scientists.
Author: Jon Lee Publisher: Springer Science & Business Media ISBN: 1461419271 Category : Mathematics Languages : en Pages : 687
Book Description
Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions. Mixed-integer nonlinear programming (MINLP) problems combine the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is one of the most flexible modeling paradigms available for optimization; but because its scope is so broad, in the most general cases it is hopelessly intractable. Nonetheless, an expanding body of researchers and practitioners — including chemical engineers, operations researchers, industrial engineers, mechanical engineers, economists, statisticians, computer scientists, operations managers, and mathematical programmers — are interested in solving large-scale MINLP instances.
Author: John C. Nash Publisher: CRC Press ISBN: 9780852743195 Category : Mathematics Languages : en Pages : 298
Book Description
This second edition of Compact Numerical Methods for Computers presents reliable yet compact algorithms for computational problems. As in the previous edition, the author considers specific mathematical problems of wide applicability, develops approaches to a solution and the consequent algorithm, and provides the program steps. He emphasizes useful applicable methods from various scientific research fields, ranging from mathematical physics to commodity production modeling. While the ubiquitous personal computer is the particular focus, the methods have been implemented on computers as small as a programmable pocket calculator and as large as a highly parallel supercomputer. New to the Second Edition Presents program steps as Turbo Pascal code Includes more algorithmic examples Contains an extended bibliography The accompanying software (available by coupon at no charge) includes not only the algorithm source codes, but also driver programs, example data, and several utility codes to help in the software engineering of end-user programs. The codes are designed for rapid implementation and reliable use in a wide variety of computing environments. Scientists, statisticians, engineers, and economists who prepare/modify programs for use in their work will find this resource invaluable. Moreover, since little previous training in numerical analysis is required, the book can also be used as a supplementary text for courses on numerical methods and mathematical software.
Author: Ralph John Waterman
Author: Ralph John Waterman
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Author: United States. National Bureau of Standards
Author: Mokhtar S. Bazaraa
Author: Olvi L. Mangasarian
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Author: 
Author: J. M. Mulvey
Author: Jon Lee
Author: John C. Nash