Studies in Linear and Non-linear Programming PDF Download
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Author: Kenneth Joseph Arrow
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 252
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Book Description
A theorem on convex polyhedral cones / Hirofumi Uzawa -- The Kuhn-Tucker theorem in concave programming / Hirofumi Uzawa -- Programming in linear spaces / Leonid Hurwicz -- A note on the Lagrangian saddle-points / Leonid Hurwicz and Hirofumi Uzawa -- Gradient method for concave programming, I: local results / Kenneth J. Arrow and Leonid Hurwicz -- Gradient method for concave programming, II: global stability in the strictly concave case / Hirofumi Uzawa -- Gradient method for concave programming, III: further global results and applications to resource allocation / Kenneth J. Arrow and Leonid Hurwicz -- An example of a modified gradient method for linear programming / Thomas Marschak -- Iterative methods for concave programming / Hirofumi Uzawa -- Gradient methods for constrained maxima, with weakened assumptions / Kenneth J. Arrow and Robert M. Solow -- An elementary method for linear programming / Hirofumi Uzawa -- Price speculation under certainty / Kenneth J. Arrow and Samuel Karlin -- A feasibility algorithm for one-way substitution in process analysis / Kenneth J. Arrow and Selmer M. Johnson -- Non-linear programming in economic development / Hollis B. Chenery and Hirofumi Uzawa.
Author: Kenneth Joseph Arrow
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 252
Get Book Here
Book Description
A theorem on convex polyhedral cones / Hirofumi Uzawa -- The Kuhn-Tucker theorem in concave programming / Hirofumi Uzawa -- Programming in linear spaces / Leonid Hurwicz -- A note on the Lagrangian saddle-points / Leonid Hurwicz and Hirofumi Uzawa -- Gradient method for concave programming, I: local results / Kenneth J. Arrow and Leonid Hurwicz -- Gradient method for concave programming, II: global stability in the strictly concave case / Hirofumi Uzawa -- Gradient method for concave programming, III: further global results and applications to resource allocation / Kenneth J. Arrow and Leonid Hurwicz -- An example of a modified gradient method for linear programming / Thomas Marschak -- Iterative methods for concave programming / Hirofumi Uzawa -- Gradient methods for constrained maxima, with weakened assumptions / Kenneth J. Arrow and Robert M. Solow -- An elementary method for linear programming / Hirofumi Uzawa -- Price speculation under certainty / Kenneth J. Arrow and Samuel Karlin -- A feasibility algorithm for one-way substitution in process analysis / Kenneth J. Arrow and Selmer M. Johnson -- Non-linear programming in economic development / Hollis B. Chenery and Hirofumi Uzawa.
Author: Richard W. Cottle
Publisher: Springer
ISBN: 1493970550
Category : Business & Economics
Languages : en
Pages : 644
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Book Description
This textbook on Linear and Nonlinear Optimization is intended for graduate and advanced undergraduate students in operations research and related fields. It is both literate and mathematically strong, yet requires no prior course in optimization. As suggested by its title, the book is divided into two parts covering in their individual chapters LP Models and Applications; Linear Equations and Inequalities; The Simplex Algorithm; Simplex Algorithm Continued; Duality and the Dual Simplex Algorithm; Postoptimality Analyses; Computational Considerations; Nonlinear (NLP) Models and Applications; Unconstrained Optimization; Descent Methods; Optimality Conditions; Problems with Linear Constraints; Problems with Nonlinear Constraints; Interior-Point Methods; and an Appendix covering Mathematical Concepts. Each chapter ends with a set of exercises. The book is based on lecture notes the authors have used in numerous optimization courses the authors have taught at Stanford University. It emphasizes modeling and numerical algorithms for optimization with continuous (not integer) variables. The discussion presents the underlying theory without always focusing on formal mathematical proofs (which can be found in cited references). Another feature of this book is its inclusion of cultural and historical matters, most often appearing among the footnotes. "This book is a real gem. The authors do a masterful job of rigorously presenting all of the relevant theory clearly and concisely while managing to avoid unnecessary tedious mathematical details. This is an ideal book for teaching a one or two semester masters-level course in optimization – it broadly covers linear and nonlinear programming effectively balancing modeling, algorithmic theory, computation, implementation, illuminating historical facts, and numerous interesting examples and exercises. Due to the clarity of the exposition, this book also serves as a valuable reference for self-study." Professor Ilan Adler, IEOR Department, UC Berkeley "A carefully crafted introduction to the main elements and applications of mathematical optimization. This volume presents the essential concepts of linear and nonlinear programming in an accessible format filled with anecdotes, examples, and exercises that bring the topic to life. The authors plumb their decades of experience in optimization to provide an enriching layer of historical context. Suitable for advanced undergraduates and masters students in management science, operations research, and related fields." Michael P. Friedlander, IBM Professor of Computer Science, Professor of Mathematics, University of British Columbia
Author: Katta G. Murty
Publisher:
ISBN:
Category : Linear complementarity problem
Languages : en
Pages : 708
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Book Description
Author: Dimitri P. Bertsekas
Publisher: Goodman Publishers
ISBN:
Category : Mathematics
Languages : en
Pages : 808
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Book Description
Author: Peter Zörnig
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110372517
Category : Mathematics
Languages : en
Pages : 402
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Book Description
This book is an introduction to nonlinear programming. It deals with the theoretical foundations and solution methods, beginning with the classical procedures and reaching up to “modern” methods like trust region methods or procedures for nonlinear and global optimization. A comprehensive bibliography including diverse web sites with information about nonlinear programming, in particular software, is presented. Without sacrificing the necessary mathematical rigor, excessive formalisms are avoided. Several examples, exercises with detailed solutions, and applications are provided, making the text adequate for individual studies. The book is written for students from the fields of applied mathematics, engineering, economy, and computation.
Author: David G. Luenberger
Publisher: Springer Science & Business Media
ISBN: 0387745033
Category : Business & Economics
Languages : en
Pages : 546
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Book Description
This third edition of the classic textbook in Optimization has been fully revised and updated. It comprehensively covers modern theoretical insights in this crucial computing area, and will be required reading for analysts and operations researchers in a variety of fields. The book connects the purely analytical character of an optimization problem, and the behavior of algorithms used to solve it. Now, the third edition has been completely updated with recent Optimization Methods. The book also has a new co-author, Yinyu Ye of California’s Stanford University, who has written lots of extra material including some on Interior Point Methods.
Author: Jerome Bracken
Publisher: New York : Wiley
ISBN:
Category : Mathematics
Languages : en
Pages : 136
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Book Description
Author: Andrzej Ruszczynski
Publisher: Princeton University Press
ISBN: 1400841054
Category : Mathematics
Languages : en
Pages : 463
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Book Description
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern topics such as optimality conditions and numerical methods for problems involving nondifferentiable functions, semidefinite programming, metric regularity and stability theory of set-constrained systems, and sensitivity analysis of optimization problems. Based on a decade's worth of notes the author compiled in successfully teaching the subject, this book will help readers to understand the mathematical foundations of the modern theory and methods of nonlinear optimization and to analyze new problems, develop optimality theory for them, and choose or construct numerical solution methods. It is a must for anyone seriously interested in optimization.
Author: Jon Lee
Publisher: Springer Science & Business Media
ISBN: 1461419271
Category : Mathematics
Languages : en
Pages : 687
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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: Kaisa Miettinen
Publisher: Springer Science & Business Media
ISBN: 1461555639
Category : Business & Economics
Languages : en
Pages : 304
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Book Description
Problems with multiple objectives and criteria are generally known as multiple criteria optimization or multiple criteria decision-making (MCDM) problems. So far, these types of problems have typically been modelled and solved by means of linear programming. However, many real-life phenomena are of a nonlinear nature, which is why we need tools for nonlinear programming capable of handling several conflicting or incommensurable objectives. In this case, methods of traditional single objective optimization and linear programming are not enough; we need new ways of thinking, new concepts, and new methods - nonlinear multiobjective optimization. Nonlinear Multiobjective Optimization provides an extensive, up-to-date, self-contained and consistent survey, review of the literature and of the state of the art on nonlinear (deterministic) multiobjective optimization, its methods, its theory and its background. The amount of literature on multiobjective optimization is immense. The treatment in this book is based on approximately 1500 publications in English printed mainly after the year 1980. Problems related to real-life applications often contain irregularities and nonsmoothnesses. The treatment of nondifferentiable multiobjective optimization in the literature is rather rare. For this reason, this book contains material about the possibilities, background, theory and methods of nondifferentiable multiobjective optimization as well. This book is intended for both researchers and students in the areas of (applied) mathematics, engineering, economics, operations research and management science; it is meant for both professionals and practitioners in many different fields of application. The intention has been to provide a consistent summary that may help in selecting an appropriate method for the problem to be solved. It is hoped the extensive bibliography will be of value to researchers.
