Linear Programming Duality

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Linear Optimization and Duality

Craig A. Tovey
Linear Optimization and Duality Book PDF

Author : Craig A. Tovey
Publisher : CRC Press
Page : 587 pages
File Size : 46,7 Mb
Release : 2020-12-15
Category : Business & Economics
ISBN : 9781439887479

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Linear Optimization and Duality by Craig A. Tovey Pdf

Linear Optimization and Dualiyy: A Modern Exposition departs from convention in significant ways. Standard linear programming textbooks present the material in the order in which it was discovered. Duality is treated as a difficult add-on after coverage of formulation, the simplex method, and polyhedral theory. Students end up without knowing duality in their bones. This text brings in duality in Chapter 1 and carries duality all the way through the exposition. Chapter 1 gives a general definition of duality that shows the dual aspects of a matrix as a column of rows and a row of columns. The proof of weak duality in Chapter 2 is shown via the Lagrangian, which relies on matrix duality. The first three LP formulation examples in Chapter 3 are classic primal-dual pairs including the diet problem and 2-person zero sum games. For many engineering students, optimization is their first immersion in rigorous mathematics. Conventional texts assume a level of mathematical sophistication they don’t have. This text embeds dozens of reading tips and hundreds of answered questions to guide such students. Features Emphasis on duality throughout Practical tips for modeling and computation Coverage of computational complexity and data structures Exercises and problems based on the learning theory concept of the zone of proximal development Guidance for the mathematically unsophisticated reader About the Author Craig A. Tovey is a professor in the H. Milton Stewart School of Industrial and Systems Engineering at Georgia Institute of Technology. Dr. Tovey received an AB from Harvard College, an MS in computer science and a PhD in operations research from Stanford University. His principal activities are in operations research and its interdisciplinary applications. He received a Presidential Young Investigator Award and the Jacob Wolfowitz Prize for research in heuristics. He was named an Institute Fellow at Georgia Tech, and was recognized by the ACM Special Interest Group on Electronic Commerce with the Test of Time Award. Dr. Tovey received the 2016 Golden Goose Award for his research on bee foraging behavior leading to the development of the Honey Bee Algorithm.

Linear Programming Duality

Achim Bachem,Walter Kern
Linear Programming Duality Book PDF

Author : Achim Bachem,Walter Kern
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642581526

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Linear Programming Duality by Achim Bachem,Walter Kern Pdf

This book presents an elementary introduction to the theory of oriented matroids. The way oriented matroids are intro- duced emphasizes that they are the most general - and hence simplest - structures for which linear Programming Duality results can be stated and proved. The main theme of the book is duality. Using Farkas' Lemma as the basis the authors start withre- sults on polyhedra in Rn and show how to restate the essence of the proofs in terms of sign patterns of oriented ma- troids. Most of the standard material in Linear Programming is presented in the setting of real space as well as in the more abstract theory of oriented matroids. This approach clarifies the theory behind Linear Programming and proofs become simpler. The last part of the book deals with the facial structure of polytopes respectively their oriented matroid counterparts. It is an introduction to more advanced topics in oriented matroid theory. Each chapter contains suggestions for furt- herreading and the references provide an overview of the research in this field.

Linear Programming with Duals

Craig A. Tovey
Linear Programming with Duals Book PDF

Author : Craig A. Tovey
Publisher : Chapman and Hall/CRC
Page : 0 pages
File Size : 46,7 Mb
Release : 2017-06-15
Category : Business & Economics
ISBN : 1439887462

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Linear Programming with Duals by Craig A. Tovey Pdf

This textbook presents a theoretical treatment of linear programming, network flows and applications, integer programming, and computational complexity. The author includes a rigorous discussion of theory, numerous examples and exercises, and geometric intuitive explanations. He also offers computational tips and interpretation of software input. Unlike other books, this text incorporates duality throughout its chapters, rather than treating it as an add-on topic. It also discusses computational complexity theory, which can be used to classify problems according to the appropriate solution method.

Linear Programming and Resource Allocation Modeling

Michael J. Panik
Linear Programming and Resource Allocation Modeling Book PDF

Author : Michael J. Panik
Publisher : John Wiley & Sons
Page : 448 pages
File Size : 44,8 Mb
Release : 2018-10-25
Category : Business & Economics
ISBN : 9781119509462

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Linear Programming and Resource Allocation Modeling by Michael J. Panik Pdf

Guides in the application of linear programming to firm decision making, with the goal of giving decision-makers a better understanding of methods at their disposal Useful as a main resource or as a supplement in an economics or management science course, this comprehensive book addresses the deficiencies of other texts when it comes to covering linear programming theory—especially where data envelopment analysis (DEA) is concerned—and provides the foundation for the development of DEA. Linear Programming and Resource Allocation Modeling begins by introducing primal and dual problems via an optimum product mix problem, and reviews the rudiments of vector and matrix operations. It then goes on to cover: the canonical and standard forms of a linear programming problem; the computational aspects of linear programming; variations of the standard simplex theme; duality theory; single- and multiple- process production functions; sensitivity analysis of the optimal solution; structural changes; and parametric programming. The primal and dual problems are then reformulated and re-examined in the context of Lagrangian saddle points, and a host of duality and complementary slackness theorems are offered. The book also covers primal and dual quadratic programs, the complementary pivot method, primal and dual linear fractional functional programs, and (matrix) game theory solutions via linear programming, and data envelopment analysis (DEA). This book: Appeals to those wishing to solve linear optimization problems in areas such as economics, business administration and management, agriculture and energy, strategic planning, public decision making, and health care Fills the need for a linear programming applications component in a management science or economics course Provides a complete treatment of linear programming as applied to activity selection and usage Contains many detailed example problems as well as textual and graphical explanations Linear Programming and Resource Allocation Modeling is an excellent resource for professionals looking to solve linear optimization problems, and advanced undergraduate to beginning graduate level management science or economics students.

Linear Programming

Robert J Vanderbei
Linear Programming Book PDF

Author : Robert J Vanderbei
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 45,9 Mb
Release : 2013-07-16
Category : Business & Economics
ISBN : 9781461476306

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Linear Programming by Robert J Vanderbei Pdf

This Fourth Edition introduces the latest theory and applications in optimization. It emphasizes constrained optimization, beginning with a substantial treatment of linear programming and then proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. Readers will discover a host of practical business applications as well as non-business applications. Topics are clearly developed with many numerical examples worked out in detail. Specific examples and concrete algorithms precede more abstract topics. With its focus on solving practical problems, the book features free C programs to implement the major algorithms covered, including the two-phase simplex method, primal-dual simplex method, path-following interior-point method, and homogeneous self-dual methods. In addition, the author provides online JAVA applets that illustrate various pivot rules and variants of the simplex method, both for linear programming and for network flows. These C programs and JAVA tools can be found on the book's website. The website also includes new online instructional tools and exercises.

Extremal Methods and Systems Analysis

A. V. Fiacco,K. O. Kortanek
Extremal Methods and Systems Analysis Book PDF

Author : A. V. Fiacco,K. O. Kortanek
Publisher : Springer Science & Business Media
Page : 554 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642464140

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Extremal Methods and Systems Analysis by A. V. Fiacco,K. O. Kortanek Pdf

The papers appearing in this Volume were selected from a collec tion of papers presented at the Internationa~ Symposium on Extrema~ Methods and Systems Ana~ysis on the Occasion of Professor A. Charnes' 60th Birthday, at the University of Texas in Austin, 13-15 September 1977. As coeditors, we have followed the normal editorial procedures of scholarly journals. We have obtained invaluable assistance from a number of colleagues who essentially performed the duties of associate editors, coordinating most of the reviews. All papers except those appearing in the Historica~ Perspectives section were refereed by at least two individuals with competency in the respective area. Because of the wide range and diversity of the topics, it would have been im possible for us to make a consistently rational selection of papers without the help of the associate editors and referees. We are indeed grateful to them. The breadth of extremal methods and systems analysis, suggested by the range of topics covered in these papers, is characteristic of the field and also of the scholarly work of Professor Charnes. Extre mal methods and systems analysis has been a pioneering and systematic approach to the development and application of new scientific theories and methods for problems of management and operations in both the pri vate and public sectors, spanning all major disciplines from economics to engineering.

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 : 55,9 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.

Semi-Infinite Programming

Miguel Ángel Goberna,Marco A. López
Semi Infinite Programming Book PDF

Author : Miguel Ángel Goberna,Marco A. López
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 50,8 Mb
Release : 2013-11-11
Category : Computers
ISBN : 9781475734034

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Semi-Infinite Programming by Miguel Ángel Goberna,Marco A. López Pdf

Semi-infinite programming (SIP) deals with optimization problems in which either the number of decision variables or the number of constraints is finite. This book presents the state of the art in SIP in a suggestive way, bringing the powerful SIP tools close to the potential users in different scientific and technological fields. The volume is divided into four parts. Part I reviews the first decade of SIP (1962-1972). Part II analyses convex and generalised SIP, conic linear programming, and disjunctive programming. New numerical methods for linear, convex, and continuously differentiable SIP problems are proposed in Part III. Finally, Part IV provides an overview of the applications of SIP to probability, statistics, experimental design, robotics, optimization under uncertainty, production games, and separation problems. Audience: This book is an indispensable reference and source for advanced students and researchers in applied mathematics and engineering.

Linear and Integer Programming vs Linear Integration and Counting

Jean-Bernard Lasserre
Linear and Integer Programming vs Linear Integration and Counting Book PDF

Author : Jean-Bernard Lasserre
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 43,5 Mb
Release : 2009-04-21
Category : Business & Economics
ISBN : 9780387094144

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Linear and Integer Programming vs Linear Integration and Counting by Jean-Bernard Lasserre Pdf

This book analyzes and compares four closely related problems, namely linear programming, integer programming, linear integration, and linear summation (or counting). The book provides some new insights on duality concepts for integer programs.

Robust Optimization

Aharon Ben-Tal,Laurent El Ghaoui,Arkadi Nemirovski
Robust Optimization Book PDF

Author : Aharon Ben-Tal,Laurent El Ghaoui,Arkadi Nemirovski
Publisher : Princeton University Press
Page : 576 pages
File Size : 55,7 Mb
Release : 2009-08-10
Category : Mathematics
ISBN : 9781400831050

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Robust Optimization by Aharon Ben-Tal,Laurent El Ghaoui,Arkadi Nemirovski Pdf

Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject.

Linear Programming in Infinite-dimensional Spaces

Edward J. Anderson,Peter Nash
Linear Programming in Infinite dimensional Spaces Book PDF

Author : Edward J. Anderson,Peter Nash
Publisher : John Wiley & Sons
Page : 194 pages
File Size : 46,9 Mb
Release : 1987
Category : Mathematics
ISBN : UOM:39015012752013

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Linear Programming in Infinite-dimensional Spaces by Edward J. Anderson,Peter Nash Pdf

Infinite-dimensional linear programs; Algebraic fundamentals; Topology and duality. Semi-infinite linear programs; The mass-transfer problem; Maximal flow in a dynamic network; Continuous linear programs; Other infinite linear programs; Index.

Understanding and Using Linear Programming

Jiri Matousek,Bernd Gärtner
Understanding and Using Linear Programming Book PDF

Author : Jiri Matousek,Bernd Gärtner
Publisher : Springer Science & Business Media
Page : 230 pages
File Size : 40,9 Mb
Release : 2007-07-04
Category : Mathematics
ISBN : 9783540307174

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Understanding and Using Linear Programming by Jiri Matousek,Bernd Gärtner Pdf

The book is an introductory textbook mainly for students of computer science and mathematics. Our guiding phrase is "what every theoretical computer scientist should know about linear programming". A major focus is on applications of linear programming, both in practice and in theory. The book is concise, but at the same time, the main results are covered with complete proofs and in sufficient detail, ready for presentation in class. The book does not require more prerequisites than basic linear algebra, which is summarized in an appendix. One of its main goals is to help the reader to see linear programming "behind the scenes".

Linear Programming with MATLAB

Michael C. Ferris,Olvi L. Mangasarian,Stephen J. Wright
Linear Programming with MATLAB Book PDF

Author : Michael C. Ferris,Olvi L. Mangasarian,Stephen J. Wright
Publisher : SIAM
Page : 270 pages
File Size : 52,6 Mb
Release : 2007-01-01
Category : Mathematics
ISBN : 9780898716436

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Linear Programming with MATLAB by Michael C. Ferris,Olvi L. Mangasarian,Stephen J. Wright Pdf

A self-contained introduction to linear programming using MATLAB® software to elucidate the development of algorithms and theory. Exercises are included in each chapter, and additional information is provided in two appendices and an accompanying Web site. Only a basic knowledge of linear algebra and calculus is required.

Linear and Nonlinear Optimization

Richard W. Cottle,Mukund N. Thapa
Linear and Nonlinear Optimization Book PDF

Author : Richard W. Cottle,Mukund N. Thapa
Publisher : Springer
Page : 614 pages
File Size : 51,9 Mb
Release : 2017-06-11
Category : Business & Economics
ISBN : 9781493970551

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Linear and Nonlinear Optimization by Richard W. Cottle,Mukund N. Thapa Pdf

​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

Encyclopedia of Operations Research and Management Science

Saul I. Gass,Carl M. Harris
Encyclopedia of Operations Research and Management Science Book PDF

Author : Saul I. Gass,Carl M. Harris
Publisher : Springer Science & Business Media
Page : 774 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9781461304593

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Encyclopedia of Operations Research and Management Science by Saul I. Gass,Carl M. Harris Pdf

Operations Research: 1934-1941," 35, 1, 143-152; "British The goal of the Encyclopedia of Operations Research and Operational Research in World War II," 35, 3, 453-470; Management Science is to provide to decision makers and "U. S. Operations Research in World War II," 35, 6, 910-925; problem solvers in business, industry, government and and the 1984 article by Harold Lardner that appeared in academia a comprehensive overview of the wide range of Operations Research: "The Origin of Operational Research," ideas, methodologies, and synergistic forces that combine to 32, 2, 465-475. form the preeminent decision-aiding fields of operations re search and management science (OR/MS). To this end, we The Encyclopedia contains no entries that define the fields enlisted a distinguished international group of academics of operations research and management science. OR and MS and practitioners to contribute articles on subjects for are often equated to one another. If one defines them by the which they are renowned. methodologies they employ, the equation would probably The editors, working with the Encyclopedia's Editorial stand inspection. If one defines them by their historical Advisory Board, surveyed and divided OR/MS into specific developments and the classes of problems they encompass, topics that collectively encompass the foundations, applica the equation becomes fuzzy. The formalism OR grew out of tions, and emerging elements of this ever-changing field. We the operational problems of the British and U. s. military also wanted to establish the close associations that OR/MS efforts in World War II.