Linear Programming Mathematics Theory And Algorithms

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Linear Programming: Mathematics, Theory and Algorithms

M.J. Panik
Linear Programming Mathematics Theory and Algorithms Book PDF

Author : M.J. Panik
Publisher : Springer Science & Business Media
Page : 502 pages
File Size : 43,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461334347

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Linear Programming: Mathematics, Theory and Algorithms by M.J. Panik Pdf

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.

Linear Programming: Mathematics, Theory and Algorithms

M.J. Panik
Linear Programming Mathematics Theory and Algorithms Book PDF

Author : M.J. Panik
Publisher : Springer
Page : 498 pages
File Size : 52,8 Mb
Release : 1995-12-31
Category : Mathematics
ISBN : 0792337824

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Linear Programming: Mathematics, Theory and Algorithms by M.J. Panik Pdf

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.

Mathematical Programming

Michel Minoux
Mathematical Programming Book PDF

Author : Michel Minoux
Publisher : John Wiley & Sons
Page : 526 pages
File Size : 40,7 Mb
Release : 1986
Category : Mathematics
ISBN : UOM:39015072616876

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Mathematical Programming by Michel Minoux Pdf

This comprehensive work covers the whole field of mathematical programming, including linear programming, unconstrained and constrained nonlinear programming, nondifferentiable (or nonsmooth) optimization, integer programming, large scale systems optimization, dynamic programming, and optimization in infinite dimensions. Special emphasis is placed on unifying concepts such as point-to-set maps, saddle points and perturbations functions, duality theory and its extensions.

Linear Programming

Yaromir Truma
Linear Programming Book PDF

Author : Yaromir Truma
Publisher : Nova Science Publishers
Page : 0 pages
File Size : 50,9 Mb
Release : 2014
Category : Linear programming
ISBN : 1631174738

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Linear Programming by Yaromir Truma Pdf

Linear programming (LP), as a specific case of mathematical programming, has been widely encountered in a broad class of scientific disciplines and engineering applications. In view of its fundamental role, the solution of LP has been investigated extensively for the past decades. Due to the parallel-distributed processing nature and circuit-implementation convenience, the neurodynamic solvers based on recurrent neural network (RNN) have been regarded as powerful alternatives to online computation. This book discusses how linear programming is used to plan and schedule the workforce in an emergency room; the neurodynamic solvers, robotic applications, and solution non-uniqueness of linear programming; the mathematical equivalence of simple recourse and chance constraints in linear stochastic programming; and provides a decomposable linear programming model for energy supply chains.

Theory and Algorithms for Linear Optimization

Cornelis Roos,T. Terlaky,J.-Ph. Vial
Theory and Algorithms for Linear Optimization Book PDF

Author : Cornelis Roos,T. Terlaky,J.-Ph. Vial
Publisher : Unknown
Page : 520 pages
File Size : 41,5 Mb
Release : 1997-03-04
Category : Mathematics
ISBN : STANFORD:36105019761993

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Theory and Algorithms for Linear Optimization by Cornelis Roos,T. Terlaky,J.-Ph. Vial Pdf

The approach to LO in this book is new in many aspects. In particular the IPM based development of duality theory is surprisingly elegant. The algorithmic parts of the book contain a complete discussion of many algorithmic variants, including predictor-corrector methods, partial updating, higher order methods and sensitivity and parametric analysis.

Mathematical Theory of Optimization

Ding-Zhu Du,Panos M. Pardalos,Weili Wu
Mathematical Theory of Optimization Book PDF

Author : Ding-Zhu Du,Panos M. Pardalos,Weili Wu
Publisher : Springer Science & Business Media
Page : 277 pages
File Size : 45,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475757958

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Mathematical Theory of Optimization by Ding-Zhu Du,Panos M. Pardalos,Weili Wu Pdf

This book provides an introduction to the mathematical theory of optimization. It emphasizes the convergence theory of nonlinear optimization algorithms and applications of nonlinear optimization to combinatorial optimization. Mathematical Theory of Optimization includes recent developments in global convergence, the Powell conjecture, semidefinite programming, and relaxation techniques for designs of approximation solutions of combinatorial optimization problems.

Nonlinear Programming

Mokhtar S. Bazaraa,Hanif D. Sherali,C. M. Shetty
Nonlinear Programming Book PDF

Author : Mokhtar S. Bazaraa,Hanif D. Sherali,C. M. Shetty
Publisher : John Wiley & Sons
Page : 867 pages
File Size : 43,7 Mb
Release : 2013-06-12
Category : Mathematics
ISBN : 9781118626306

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Nonlinear Programming by Mokhtar S. Bazaraa,Hanif D. Sherali,C. M. Shetty Pdf

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.

Linear Programming

Howard Karloff
Linear Programming Book PDF

Author : Howard Karloff
Publisher : Springer Science & Business Media
Page : 150 pages
File Size : 45,6 Mb
Release : 2008-10-14
Category : Computers
ISBN : 9780817648442

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Linear Programming by Howard Karloff Pdf

To this reviewer’s knowledge, this is the first book accessible to the upper division undergraduate or beginning graduate student that surveys linear programming.... Style is informal. ...Recommended highly for acquisition, since it is not only a textbook, but can also be used for independent reading and study. —Choice Reviews This is a textbook intended for advanced undergraduate or graduate students. It contains both theory and computational practice. —Zentralblatt Math

An Introduction to Linear Programming and Game Theory

Paul R. Thie,Gerard E. Keough
An Introduction to Linear Programming and Game Theory Book PDF

Author : Paul R. Thie,Gerard E. Keough
Publisher : John Wiley & Sons
Page : 476 pages
File Size : 52,6 Mb
Release : 2011-09-15
Category : Mathematics
ISBN : 9781118165454

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An Introduction to Linear Programming and Game Theory by Paul R. Thie,Gerard E. Keough Pdf

Praise for the Second Edition: "This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications." —Mathematical Reviews of the American Mathematical Society An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the social, life, and managerial sciences, providing readers with the opportunity to develop and apply their analytical abilities when solving realistic problems. This Third Edition addresses various new topics and improvements in the field of mathematical programming, and it also presents two software programs, LP Assistant and the Solver add-in for Microsoft Office Excel, for solving linear programming problems. LP Assistant, developed by coauthor Gerard Keough, allows readers to perform the basic steps of the algorithms provided in the book and is freely available via the book's related Web site. The use of the sensitivity analysis report and integer programming algorithm from the Solver add-in for Microsoft Office Excel is introduced so readers can solve the book's linear and integer programming problems. A detailed appendix contains instructions for the use of both applications. Additional features of the Third Edition include: A discussion of sensitivity analysis for the two-variable problem, along with new examples demonstrating integer programming, non-linear programming, and make vs. buy models Revised proofs and a discussion on the relevance and solution of the dual problem A section on developing an example in Data Envelopment Analysis An outline of the proof of John Nash's theorem on the existence of equilibrium strategy pairs for non-cooperative, non-zero-sum games Providing a complete mathematical development of all presented concepts and examples, Introduction to Linear Programming and Game Theory, Third Edition is an ideal text for linear programming and mathematical modeling courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for professionals who use game theory in business, economics, and management science.

Algorithmic Principles of Mathematical Programming

Ulrich Faigle,W. Kern,G. Still
Algorithmic Principles of Mathematical Programming Book PDF

Author : Ulrich Faigle,W. Kern,G. Still
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 51,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401598965

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Algorithmic Principles of Mathematical Programming by Ulrich Faigle,W. Kern,G. Still Pdf

Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear programming, and nonlinear optimization are closely linked. This book offers a comprehensive introduction to the whole subject and leads the reader to the frontiers of current research. The prerequisites to use the book are very elementary. All the tools from numerical linear algebra and calculus are fully reviewed and developed. Rather than attempting to be encyclopedic, the book illustrates the important basic techniques with typical problems. The focus is on efficient algorithms with respect to practical usefulness. Algorithmic complexity theory is presented with the goal of helping the reader understand the concepts without having to become a theoretical specialist. Further theory is outlined and supplemented with pointers to the relevant literature.

Linear Programming

S. Vajda
Linear Programming Book PDF

Author : S. Vajda
Publisher : Springer Science & Business Media
Page : 156 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9789401169240

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Linear Programming by S. Vajda Pdf

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 some combinatorial theory as well. The chapters on duality, and on flow in networks, are particularly directed towards this aim and they contain theorems which might not be directly relevant to methods of computation. The application of the concept of duality to the theory of games is of historical interest. It is hoped that the figures, which illustrate the results, will be found illuminating by readers with active geometrical imagination.

Progress in Mathematical Programming

Nimrod Megiddo
Progress in Mathematical Programming Book PDF

Author : Nimrod Megiddo
Publisher : Springer Science & Business Media
Page : 164 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461396178

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Progress in Mathematical Programming by Nimrod Megiddo Pdf

The starting point of this volume was a conference entitled "Progress in Mathematical Programming," held at the Asilomar Conference Center in Pacific Grove, California, March 1-4, 1987. The main topic of the conference was developments in the theory and practice of linear programming since Karmarkar's algorithm. There were thirty presentations and approximately fifty people attended. Presentations included new algorithms, new analyses of algorithms, reports on computational experience, and some other topics related to the practice of mathematical programming. Interestingly, most of the progress reported at the conference was on the theoretical side. Several new polynomial algorithms for linear program ming were presented (Barnes-Chopra-Jensen, Goldfarb-Mehrotra, Gonzaga, Kojima-Mizuno-Yoshise, Renegar, Todd, Vaidya, and Ye). Other algorithms presented were by Betke-Gritzmann, Blum, Gill-Murray-Saunders-Wright, Nazareth, Vial, and Zikan-Cottle. Efforts in the theoretical analysis of algo rithms were also reported (Anstreicher, Bayer-Lagarias, Imai, Lagarias, Megiddo-Shub, Lagarias, Smale, and Vanderbei). Computational experiences were reported by Lustig, Tomlin, Todd, Tone, Ye, and Zikan-Cottle. Of special interest, although not in the main direction discussed at the conference, was the report by Rinaldi on the practical solution of some large traveling salesman problems. At the time of the conference, it was still not clear whether the new algorithms developed since Karmarkar's algorithm would replace the simplex method in practice. Alan Hoffman presented results on conditions under which linear programming problems can be solved by greedy algorithms."

Potential Function Methods for Approximately Solving Linear Programming Problems: Theory and Practice

Daniel Bienstock
Potential Function Methods for Approximately Solving Linear Programming Problems Theory and Practice Book PDF

Author : Daniel Bienstock
Publisher : Springer
Page : 111 pages
File Size : 54,9 Mb
Release : 2013-03-26
Category : Mathematics
ISBN : 1475776713

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Potential Function Methods for Approximately Solving Linear Programming Problems: Theory and Practice by Daniel Bienstock Pdf

Potential Function Methods For Approximately Solving Linear Programming Problems breaks new ground in linear programming theory. The book draws on the research developments in three broad areas: linear and integer programming, numerical analysis, and the computational architectures which enable speedy, high-level algorithm design. During the last ten years, a new body of research within the field of optimization research has emerged, which seeks to develop good approximation algorithms for classes of linear programming problems. This work both has roots in fundamental areas of mathematical programming and is also framed in the context of the modern theory of algorithms. The result of this work, in which Daniel Bienstock has been very much involved, has been a family of algorithms with solid theoretical foundations and with growing experimental success. This book will examine these algorithms, starting with some of the very earliest examples, and through the latest theoretical and computational developments.

Theory of Linear and Integer Programming

Alexander Schrijver
Theory of Linear and Integer Programming Book PDF

Author : Alexander Schrijver
Publisher : John Wiley & Sons
Page : 488 pages
File Size : 43,8 Mb
Release : 1998-06-11
Category : Mathematics
ISBN : 0471982326

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Theory of Linear and Integer Programming by Alexander Schrijver Pdf

Als Ergänzung zu den mehr praxisorientierten Büchern, die auf dem Gebiet der linearen und Integerprogrammierung bereits erschienen sind, beschreibt dieses Werk die zugrunde liegende Theorie und gibt einen Überblick über wichtige Algorithmen. Der Autor diskutiert auch Anwendungen auf die kombinatorische Optimierung; neben einer ausführlichen Bibliographie finden sich umfangreiche historische Anmerkungen.

Interior Point Methods of Mathematical Programming

Tamás Terlaky
Interior Point Methods of Mathematical Programming Book PDF

Author : Tamás Terlaky
Publisher : Springer Science & Business Media
Page : 544 pages
File Size : 43,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461334491

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Interior Point Methods of Mathematical Programming by Tamás Terlaky Pdf

One has to make everything as simple as possible but, never more simple. Albert Einstein Discovery consists of seeing what every body has seen and thinking what nobody has thought. Albert S. ent_Gyorgy; The primary goal of this book is to provide an introduction to the theory of Interior Point Methods (IPMs) in Mathematical Programming. At the same time, we try to present a quick overview of the impact of extensions of IPMs on smooth nonlinear optimization and to demonstrate the potential of IPMs for solving difficult practical problems. The Simplex Method has dominated the theory and practice of mathematical pro gramming since 1947 when Dantzig discovered it. In the fifties and sixties several attempts were made to develop alternative solution methods. At that time the prin cipal base of interior point methods was also developed, for example in the work of Frisch (1955), Caroll (1961), Huard (1967), Fiacco and McCormick (1968) and Dikin (1967). In 1972 Klee and Minty made explicit that in the worst case some variants of the simplex method may require an exponential amount of work to solve Linear Programming (LP) problems. This was at the time when complexity theory became a topic of great interest. People started to classify mathematical programming prob lems as efficiently (in polynomial time) solvable and as difficult (NP-hard) problems. For a while it remained open whether LP was solvable in polynomial time or not. The break-through resolution ofthis problem was obtained by Khachijan (1989).