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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: W. Hock Publisher: Springer ISBN: Category : Business & Economics Languages : en Pages : 196
Book Description
... The performance of a nonlinear programming algorithm can only be ascertained by numerical experiments requiring the collection and implementation of test examples in dependence upon the desired performance criterium. This book should be considered as an assisƯ tance for a test designer since it presents an extensive collecƯ tion of nonlinear programming problems which have been used in the past to test or compare optimization programs. He will be inƯ formed about the optimal solution, about the structure of the problem in the neighbourhood of the solution, and, in addition, about the usage of the corresp, onding FORTRAN subroutines if he is interested in obtaining them -ofi a magnetic tape. Chapter I shows how the test examples are documented. In parƯ ticular, the evaluation of computable information about the soluƯ tion of a problem is outlined. It is explained how the optimal solution, the optimal Lagrange-multipliers, and the condition number of the projected Hessian of the Lagrangian are obtained. Furthermore, a classification number is defined allowing a formal description of a test problem, and the documentation scheme is described which is used in Chapter IV to present the problems.
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: J. M. Mulvey
Author: Klaus Schittkowski
Author: W. Hock