Linear Optimization And Extensions Problems And Solutions

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Linear Optimization and Extensions

Author : Dimitris Alevras
Publisher : Springer Science & Business Media
ISBN 13 : 3642566286
Total Pages : 451 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Linear Optimization and Extensions by : Dimitris Alevras

Download or read book Linear Optimization and Extensions written by Dimitris Alevras and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: Books on a technical topic - like linear programming - without exercises ignore the principal beneficiary of the endeavor of writing a book, namely the student - who learns best by doing course. Books with exercises - if they are challenging or at least to some extent so exercises, of - need a solutions manual so that students can have recourse to it when they need it. Here we give solutions to all exercises and case studies of M. Padberg's Linear Optimization and Exten sions (second edition, Springer-Verlag, Berlin, 1999). In addition we have included several new exercises and taken the opportunity to correct and change some of the exercises of the book. Here and in the main text of the present volume the terms "book", "text" etc. designate the second edition of Padberg's LPbook and the page and formula references refer to that edition as well. All new and changed exercises are marked by a star * in this volume. The changes that we have made in the original exercises are inconsequential for the main part of the original text where several ofthe exercises (especiallyin Chapter 9) are used on several occasions in the proof arguments. None of the exercises that are used in the estimations, etc. have been changed.

Linear Optimization And Extensions: Problems And Solutions

Author : Alevras
Publisher :
ISBN 13 : 9788184895247
Total Pages : 458 pages
Book Rating : 4.8/5 (952 download)

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Book Synopsis Linear Optimization And Extensions: Problems And Solutions by : Alevras

Download or read book Linear Optimization And Extensions: Problems And Solutions written by Alevras and published by . This book was released on 2009-12-01 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive treatment of the exercises and case studies as well as summaries of the chapters of the book "Linear optimization and extension" by manfred padberg, together with several new exercises and minicases with their solutions. It covers the areas of linear programming and the optimization of linear functions over polyhedra in finite dimensional euclidean vector spaces.

Linear Optimization and Extensions

Author : Manfred Padberg
Publisher : Springer Science & Business Media
ISBN 13 : 3662122731
Total Pages : 521 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Linear Optimization and Extensions by : Manfred Padberg

Download or read book Linear Optimization and Extensions written by Manfred Padberg and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "Do you know M.Padberg's Linear Optimization and Extensions? [...] Now here is the continuation of it, discussing the solutions of all its exercises and with detailed analysis of the applications mentioned. Tell your students about it. [...] For those who strive for good exercises and case studies for LP this is an excellent volume." Acta Scientiarum Mathematicarum

Linear Optimization Problems with Inexact Data

Author : Miroslav Fiedler
Publisher : Springer Science & Business Media
ISBN 13 : 0387326987
Total Pages : 222 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Linear Optimization Problems with Inexact Data by : Miroslav Fiedler

Download or read book Linear Optimization Problems with Inexact Data written by Miroslav Fiedler and published by Springer Science & Business Media. This book was released on 2006-07-18 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear programming has attracted the interest of mathematicians since World War II when the first computers were constructed. Early attempts to apply linear programming methods practical problems failed, in part because of the inexactness of the data used to create the models. This book presents a comprehensive treatment of linear optimization with inexact data, summarizing existing results and presenting new ones within a unifying framework.

Linear Programming

Author : Robert J Vanderbei
Publisher : Springer Science & Business Media
ISBN 13 : 1461476305
Total Pages : 420 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Linear Programming by : Robert J Vanderbei

Download or read book Linear Programming written by Robert J Vanderbei and published by Springer Science & Business Media. This book was released on 2013-07-16 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Linear Optimization and Extensions

Author : Shu-Cherng Fang
Publisher :
ISBN 13 :
Total Pages : 328 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Linear Optimization and Extensions by : Shu-Cherng Fang

Download or read book Linear Optimization and Extensions written by Shu-Cherng Fang and published by . This book was released on 1993 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Linear Optimization and Extensions with MATLAB

Author : Roy H. Kwon
Publisher : CRC Press
ISBN 13 : 1482204347
Total Pages : 356 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Introduction to Linear Optimization and Extensions with MATLAB by : Roy H. Kwon

Download or read book Introduction to Linear Optimization and Extensions with MATLAB written by Roy H. Kwon and published by CRC Press. This book was released on 2013-09-05 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Filling the need for an introductory book on linear programming that discusses the important ways to mitigate parameter uncertainty, Introduction to Linear Optimization and Extensions with MATLAB provides a concrete and intuitive yet rigorous introduction to modern linear optimization. In addition to fundamental topics, the book discusses current l

Linear Optimization

Author : Glenn Hurlbert
Publisher : Springer Science & Business Media
ISBN 13 : 0387791485
Total Pages : 279 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Linear Optimization by : Glenn Hurlbert

Download or read book Linear Optimization written by Glenn Hurlbert and published by Springer Science & Business Media. This book was released on 2009-11-09 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Subject A little explanation is in order for our choice of the title Linear Opti- 1 mization (and corresponding terminology) for what has traditionally been called Linear Programming.Theword programming in this context can be confusing and/or misleading to students. Linear programming problems are referred to as optimization problems but the general term linear p- gramming remains. This can cause people unfamiliar with the subject to think that it is about programming in the sense of writing computer code. It isn’t. This workbook is about the beautiful mathematics underlying the ideas of optimizing linear functions subject to linear constraints and the algorithms to solve such problems. In particular, much of what we d- cuss is the mathematics of Simplex Algorithm for solving such problems, developed by George Dantzig in the late 1940s. The word program in linear programming is a historical artifact. When Dantzig ?rstdevelopedthe Simplex Algorithm to solvewhat arenowcalled linear programming problems, his initial model was a class of resource - location problems to be solved for the U.S. Air Force. The decisions about theallocationswerecalled‘Programs’bytheAirForce,andhencetheterm.

Linear Programming and Extensions

Author : George Dantzig
Publisher : Princeton University Press
ISBN 13 : 1400884179
Total Pages : 651 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Linear Programming and Extensions by : George Dantzig

Download or read book Linear Programming and Extensions written by George Dantzig and published by Princeton University Press. This book was released on 2016-08-10 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt: In real-world problems related to finance, business, and management, mathematicians and economists frequently encounter optimization problems. In this classic book, George Dantzig looks at a wealth of examples and develops linear programming methods for their solutions. He begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them. Treatments of the price concept, the transportation problem, and matrix methods are also given, and key mathematical concepts such as the properties of convex sets and linear vector spaces are covered. George Dantzig is properly acclaimed as the "father of linear programming." Linear programming is a mathematical technique used to optimize a situation. It can be used to minimize traffic congestion or to maximize the scheduling of airline flights. He formulated its basic theoretical model and discovered its underlying computational algorithm, the "simplex method," in a pathbreaking memorandum published by the United States Air Force in early 1948. Linear Programming and Extensions provides an extraordinary account of the subsequent development of his subject, including research in mathematical theory, computation, economic analysis, and applications to industrial problems. Dantzig first achieved success as a statistics graduate student at the University of California, Berkeley. One day he arrived for a class after it had begun, and assumed the two problems on the board were assigned for homework. When he handed in the solutions, he apologized to his professor, Jerzy Neyman, for their being late but explained that he had found the problems harder than usual. About six weeks later, Neyman excitedly told Dantzig, "I've just written an introduction to one of your papers. Read it so I can send it out right away for publication." Dantzig had no idea what he was talking about. He later learned that the "homework" problems had in fact been two famous unsolved problems in statistics.

Large Scale Linear and Integer Optimization: A Unified Approach

Author : Richard Kipp Martin
Publisher : Springer Science & Business Media
ISBN 13 : 1461549752
Total Pages : 739 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Large Scale Linear and Integer Optimization: A Unified Approach by : Richard Kipp Martin

Download or read book Large Scale Linear and Integer Optimization: A Unified Approach written by Richard Kipp Martin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook about linear and integer linear optimization. There is a growing need in industries such as airline, trucking, and financial engineering to solve very large linear and integer linear optimization problems. Building these models requires uniquely trained individuals. Not only must they have a thorough understanding of the theory behind mathematical programming, they must have substantial knowledge of how to solve very large models in today's computing environment. The major goal of the book is to develop the theory of linear and integer linear optimization in a unified manner and then demonstrate how to use this theory in a modern computing environment to solve very large real world problems. After presenting introductory material in Part I, Part II of this book is de voted to the theory of linear and integer linear optimization. This theory is developed using two simple, but unifying ideas: projection and inverse projec tion. Through projection we take a system of linear inequalities and replace some of the variables with additional linear inequalities. Inverse projection, the dual of this process, involves replacing linear inequalities with additional variables. Fundamental results such as weak and strong duality, theorems of the alternative, complementary slackness, sensitivity analysis, finite basis the orems, etc. are all explained using projection or inverse projection. Indeed, a unique feature of this book is that these fundamental results are developed and explained before the simplex and interior point algorithms are presented.

An Introduction to Linear Programming and Game Theory

Author : Paul R. Thie
Publisher : John Wiley & Sons
ISBN 13 : 1118165454
Total Pages : 476 pages
Book Rating : 4.1/5 (181 download)

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Book Synopsis An Introduction to Linear Programming and Game Theory by : Paul R. Thie

Download or read book An Introduction to Linear Programming and Game Theory written by Paul R. Thie and published by John Wiley & Sons. This book was released on 2011-09-15 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Optimization

Author : H. Ronald Miller
Publisher : John Wiley & Sons
ISBN 13 : 1118031180
Total Pages : 676 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Optimization by : H. Ronald Miller

Download or read book Optimization written by H. Ronald Miller and published by John Wiley & Sons. This book was released on 2011-03-29 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough and highly accessible resource for analysts in a broadrange of social sciences. Optimization: Foundations and Applications presents a series ofapproaches to the challenges faced by analysts who must find thebest way to accomplish particular objectives, usually with theadded complication of constraints on the available choices.Award-winning educator Ronald E. Miller provides detailed coverageof both classical, calculus-based approaches and newer,computer-based iterative methods. Dr. Miller lays a solid foundation for both linear and nonlinearmodels and quickly moves on to discuss applications, includingiterative methods for root-finding and for unconstrainedmaximization, approaches to the inequality constrained linearprogramming problem, and the complexities of inequality constrainedmaximization and minimization in nonlinear problems. Otherimportant features include: More than 200 geometric interpretations of algebraic results,emphasizing the intuitive appeal of mathematics Classic results mixed with modern numerical methods to aidusers of computer programs Extensive appendices containing mathematical details importantfor a thorough understanding of the topic With special emphasis on questions most frequently asked by thoseencountering this material for the first time, Optimization:Foundations and Applications is an extremely useful resource forprofessionals in such areas as mathematics, engineering, economicsand business, regional science, geography, sociology, politicalscience, management and decision sciences, public policy analysis,and numerous other social sciences. An Instructor's Manual presenting detailed solutions to all theproblems in the book is available upon request from the Wileyeditorial department.

The Solution of Discrete Linear Optimization Problems by Neighborhood Search Techniques

Author : Sam Linton Savage
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis The Solution of Discrete Linear Optimization Problems by Neighborhood Search Techniques by : Sam Linton Savage

Download or read book The Solution of Discrete Linear Optimization Problems by Neighborhood Search Techniques written by Sam Linton Savage and published by . This book was released on 1973 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Progress in Mathematical Programming

Author : Nimrod Megiddo
Publisher : Springer Science & Business Media
ISBN 13 : 1461396174
Total Pages : 164 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Progress in Mathematical Programming by : Nimrod Megiddo

Download or read book Progress in Mathematical Programming written by Nimrod Megiddo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."

Linear Optimization and Duality

Author : Craig A. Tovey
Publisher : CRC Press
ISBN 13 : 1351643487
Total Pages : 622 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Linear Optimization and Duality by : Craig A. Tovey

Download or read book Linear Optimization and Duality written by Craig A. Tovey and published by CRC Press. This book was released on 2020-12-16 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Optimization

Author : W. Allen Spivey
Publisher :
ISBN 13 :
Total Pages : 556 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Linear Optimization by : W. Allen Spivey

Download or read book Linear Optimization written by W. Allen Spivey and published by . This book was released on 1970 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Conical Approach to Linear Programming

Author : P D'Alessandro
Publisher : CRC Press
ISBN 13 : 9789056990312
Total Pages : 316 pages
Book Rating : 4.9/5 (93 download)

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Book Synopsis Conical Approach to Linear Programming by : P D'Alessandro

Download or read book Conical Approach to Linear Programming written by P D'Alessandro and published by CRC Press. This book was released on 1997-10-29 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conical approach provides a geometrical understanding of optimization and is a powerful research tool and useful problem-solving technique (for example, in decision support and real time control applications). Conical optimality conditions are first stated in a very general optimization framework, and then applied to linear programming. A complete theory along with primal and dual algorithms is given, and solutions and algorithms are also provided for vector and robust linear optimization. The advantages of parameter dependence of conical methods are fully discussed. In addition to numerical results, the book provides source codes and detailed documentation of a Modula-2 implementation for the main algorithms.