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| dual problem linear programming: Encyclopedia of Operations Research and Management Science Saul I. Gass, Carl M. Harris, 2012-12-06 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. |
| dual problem linear programming: Linear Programming Robert J Vanderbei, 2013-07-16 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. |
| dual problem linear programming: Linear Programming Duality Achim Bachem, Walter Kern, 1992-07-30 The main theorem of Linear Programming Duality, relating a pri- mal Linear Programming problem to its dual and vice versa, can be seen as a statement about sign patterns of vectors in complemen- tary subspaces of Rn. This observation, first made by R.T. Rockafellar in the late six- ties, led to the introduction of certain systems of sign vectors, called oriented matroids. Indeed, when oriented matroids came into being in the early seventies, one of the main issues was to study the fun- damental principles underlying Linear Progra.mrning Duality in this abstract setting. In the present book we tried to follow this approach, i.e., rather than starting out from ordinary (unoriented) matroid theory, we pre- ferred to develop oriented matroids directly as appropriate abstrac- tions of linear subspaces. Thus, the way we introduce oriented ma- troids makes clear that these structures are the most general -and hence, the most simple -ones in which Linear Programming Duality results can be stated and proved. We hope that this helps to get a better understanding of LP-Duality for those who have learned about it before und a good introduction for those who have not. |
| dual problem linear programming: Linear Programming and Resource Allocation Modeling Michael J. Panik, 2018-10-25 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. |
| dual problem linear programming: Extremal Methods and Systems Analysis A. V. Fiacco, K. O. Kortanek, 2012-12-06 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. |
| dual problem linear programming: Primal-dual Interior-Point Methods Stephen J. Wright, 1997-01-01 In the past decade, primal-dual algorithms have emerged as the most important and useful algorithms from the interior-point class. This book presents the major primal-dual algorithms for linear programming in straightforward terms. A thorough description of the theoretical properties of these methods is given, as are a discussion of practical and computational aspects and a summary of current software. This is an excellent, timely, and well-written work. The major primal-dual algorithms covered in this book are path-following algorithms (short- and long-step, predictor-corrector), potential-reduction algorithms, and infeasible-interior-point algorithms. A unified treatment of superlinear convergence, finite termination, and detection of infeasible problems is presented. Issues relevant to practical implementation are also discussed, including sparse linear algebra and a complete specification of Mehrotra's predictor-corrector algorithm. Also treated are extensions of primal-dual algorithms to more general problems such as monotone complementarity, semidefinite programming, and general convex programming problems. |
| dual problem linear programming: Linear Optimization and Duality Craig A. Tovey, 2020-12-15 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. |
| dual problem linear programming: Linear Programs and Related Problems Evar D. Nering, Albert W. Tucker, 1993 This text is concerned primarily with the theory of linear and nonlinear programming, and a number of closely-related problems, and with algorithms appropriate to those problems. In the first part of the book, the authors introduce the concept of duality which serves as a unifying concept throughout the book. The simplex algorithm is presented along with modifications and adaptations to problems with special structures. Two alternative algorithms, the ellipsoidal algorithm and Karmarker's algorithm, are also discussed, along with numerical considerations. the second part of the book looks at specific types of problems and methods for their solution. This book is designed as a textbook for mathematical programming courses, and each chapter contains numerous exercises and examples. |
| dual problem linear programming: Semi-Infinite Programming Miguel Ángel Goberna, Marco A. López, 2013-11-11 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. |
| dual problem linear programming: Linear Optimization and Extensions Manfred Padberg, 2013-04-17 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 |
| dual problem linear programming: Understanding and Using Linear Programming Jiri Matousek, Bernd Gärtner, 2007-07-04 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. |
| dual problem linear programming: An Introduction to Linear Programming and Game Theory Paul R. Thie, Gerard E. Keough, 2011-09-15 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. |
| dual problem linear programming: Linear Programming with MATLAB Michael C. Ferris, Olvi L. Mangasarian, Stephen J. Wright, 2007-01-01 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. |
| dual problem linear programming: Linear Programming with Duals Craig A. Tovey, 2017-06-15 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. |
| dual problem linear programming: Linear Programming G. V. Shenoy, 2007 Due To The Availability Of Computer Packages, The Use Of Linear Programming Technique By The Managers Has Become Universal. This Text Has Been Written Primarily For Management Students And Executives Who Have No Previous Background Of Linear Programming. The Text Is Oriented Towards Introducing Important Ideas In Linear Programming Technique At A Fundamental Level And Help The Students In Understanding Its Applications To A Wide Variety Of Managerial Problems. In Order To Strengthen The Understanding, Each Concept Has Been Illustrated With Examples. The Book Has Been Written In A Simple And Lucid Language And Has Avoided Mathematical Derivations So As To Make It Accessible To Every One.The Text Can Be Used In Its Entirely In A Fifteen Session Course At Programmes In Management, Commerce, Economics, Engineering Or Accountancy. The Text Can Be Used In One/Two Week Management/Executive Development Programmes To Be Supplemented With Some Cases. Practicing Managers And Executives, Computer Professionals, Industrial Engineers, Chartered And Cost Accountants And Economic Planners Would Also Find This Text Useful. |
| dual problem linear programming: Linear Programming Duality Achim Bachem, Walter Kern, 2012-12-06 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. |
| dual problem linear programming: Linear and Nonlinear Optimization Richard W. Cottle, Mukund N. Thapa, 2017-06-11 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 |
| dual problem linear programming: Algorithms Sanjoy Dasgupta, Christos H. Papadimitriou, Umesh Virkumar Vazirani, 2006 This text, extensively class-tested over a decade at UC Berkeley and UC San Diego, explains the fundamentals of algorithms in a story line that makes the material enjoyable and easy to digest. Emphasis is placed on understanding the crisp mathematical idea behind each algorithm, in a manner that is intuitive and rigorous without being unduly formal. Features include:The use of boxes to strengthen the narrative: pieces that provide historical context, descriptions of how the algorithms are used in practice, and excursions for the mathematically sophisticated. Carefully chosen advanced topics that can be skipped in a standard one-semester course but can be covered in an advanced algorithms course or in a more leisurely two-semester sequence.An accessible treatment of linear programming introduces students to one of the greatest achievements in algorithms. An optional chapter on the quantum algorithm for factoring provides a unique peephole into this exciting topic. In addition to the text DasGupta also offers a Solutions Manual which is available on the Online Learning Center.Algorithms is an outstanding undergraduate text equally informed by the historical roots and contemporary applications of its subject. Like a captivating novel it is a joy to read. Tim Roughgarden Stanford University |
| dual problem linear programming: Linear Programming in Infinite-dimensional Spaces Edward J. Anderson, Peter Nash, 1987 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. |
| dual problem linear programming: Column Generation Guy Desaulniers, Jacques Desrosiers, Marius M. Solomon, 2006-03-20 Column Generation is an insightful overview of the state of the art in integer programming column generation and its many applications. The volume begins with A Primer in Column Generation which outlines the theory and ideas necessary to solve large-scale practical problems, illustrated with a variety of examples. Other chapters follow this introduction on Shortest Path Problems with Resource Constraints, Vehicle Routing Problem with Time Window, Branch-and-Price Heuristics, Cutting Stock Problems, each dealing with methodological aspects of the field. Three chapters deal with transportation applications: Large-scale Models in the Airline Industry, Robust Inventory Ship Routing by Column Generation, and Ship Scheduling with Recurring Visits and Visit Separation Requirements. Production is the focus of another three chapters: Combining Column Generation and Lagrangian Relaxation, Dantzig-Wolfe Decomposition for Job Shop Scheduling, and Applying Column Generation to Machine Scheduling. The final chapter by François Vanderbeck, Implementing Mixed Integer Column Generation, reviews how to set-up the Dantzig-Wolfe reformulation, adapt standard MIP techniques to the column generation context (branching, preprocessing, primal heuristics), and deal with specific column generation issues (initialization, stabilization, column management strategies). |
| dual problem linear programming: An Economic Interpretation of Linear Programming Quirino Paris, 2016-04-29 This text covers the basic theory and computation for mathematical modeling in linear programming. It provides a strong background on how to set up mathematical proofs and high-level computation methods, and includes substantial background material and direction. Paris presents an intuitive and novel discussion of what it means to solve a system of equations that is a crucial stepping stone for solving any linear program. The discussion of the simplex method for solving linear programs gives an economic interpretation to every step of the simplex algorithm. The text combines in a unique and novel way the microeconomics of production with the structure of linear programming to give students and scholars of economics a clear notion of what it means, formulating a model of economic equilibrium and the computation of opportunity cost in the presence of many outputs and inputs. |
| dual problem linear programming: Linear and Integer Programming vs Linear Integration and Counting Jean-Bernard Lasserre, 2009-04-21 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. |
| dual problem linear programming: Elementary Linear Programming with Applications Bernard Kolman, Robert E. Beck, 2014-05-10 Elementary Linear Programming with Applications presents a survey of the basic ideas in linear programming and related areas. It also provides students with some of the tools used in solving difficult problems which will prove useful in their professional career. The text is comprised of six chapters. The Prologue gives a brief survey of operations research and discusses the different steps in solving an operations research problem. Chapter 0 gives a quick review of the necessary linear algebra. Chapter 1 deals with the basic necessary geometric ideas in Rn. Chapter 2 introduces linear programming with examples of the problems to be considered, and presents the simplex method as an algorithm for solving linear programming problems. Chapter 3 covers further topics in linear programming, including duality theory and sensitivity analysis. Chapter 4 presents an introduction to integer programming. Chapter 5 covers a few of the more important topics in network flows. Students of business, engineering, computer science, and mathematics will find the book very useful. |
| dual problem linear programming: Robust Optimization Aharon Ben-Tal, Laurent El Ghaoui, Arkadi Nemirovski, 2009-08-10 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. |
| dual problem linear programming: Applied Mathematical Programming Stephen P. Bradley, Arnoldo C. Hax, Thomas L. Magnanti, 1977 Mathematical programming: an overview; solving linear programs; sensitivity analysis; duality in linear programming; mathematical programming in practice; integration of strategic and tactical planning in the aluminum industry; planning the mission and composition of the U.S. merchant Marine fleet; network models; integer programming; design of a naval tender job shop; dynamic programming; large-scale systems; nonlinear programming; a system for bank portfolio planning; vectors and matrices; linear programming in matrix form; a labeling algorithm for the maximun-flow network problem. |
| dual problem linear programming: Linear Programming and Network Flows Mokhtar S. Bazaraa, John J. Jarvis, Hanif D. Sherali, 2011-09-28 The authoritative guide to modeling and solving complex problems with linear programming—extensively revised, expanded, and updated The only book to treat both linear programming techniques and network flows under one cover, Linear Programming and Network Flows, Fourth Edition has been completely updated with the latest developments on the topic. This new edition continues to successfully emphasize modeling concepts, the design and analysis of algorithms, and implementation strategies for problems in a variety of fields, including industrial engineering, management science, operations research, computer science, and mathematics. The book begins with basic results on linear algebra and convex analysis, and a geometrically motivated study of the structure of polyhedral sets is provided. Subsequent chapters include coverage of cycling in the simplex method, interior point methods, and sensitivity and parametric analysis. Newly added topics in the Fourth Edition include: The cycling phenomenon in linear programming and the geometry of cycling Duality relationships with cycling Elaboration on stable factorizations and implementation strategies Stabilized column generation and acceleration of Benders and Dantzig-Wolfe decomposition methods Line search and dual ascent ideas for the out-of-kilter algorithm Heap implementation comments, negative cost circuit insights, and additional convergence analyses for shortest path problems The authors present concepts and techniques that are illustrated by numerical examples along with insights complete with detailed mathematical analysis and justification. An emphasis is placed on providing geometric viewpoints and economic interpretations as well as strengthening the understanding of the fundamental ideas. Each chapter is accompanied by Notes and References sections that provide historical developments in addition to current and future trends. Updated exercises allow readers to test their comprehension of the presented material, and extensive references provide resources for further study. Linear Programming and Network Flows, Fourth Edition is an excellent book for linear programming and network flow courses at the upper-undergraduate and graduate levels. It is also a valuable resource for applied scientists who would like to refresh their understanding of linear programming and network flow techniques. |
| dual problem linear programming: Handbook of Optimization Ivan Zelinka, Vaclav Snasael, Ajith Abraham, 2012-09-26 Optimization problems were and still are the focus of mathematics from antiquity to the present. Since the beginning of our civilization, the human race has had to confront numerous technological challenges, such as finding the optimal solution of various problems including control technologies, power sources construction, applications in economy, mechanical engineering and energy distribution amongst others. These examples encompass both ancient as well as modern technologies like the first electrical energy distribution network in USA etc. Some of the key principles formulated in the middle ages were done by Johannes Kepler (Problem of the wine barrels), Johan Bernoulli (brachystochrone problem), Leonhard Euler (Calculus of Variations), Lagrange (Principle multipliers), that were formulated primarily in the ancient world and are of a geometric nature. In the beginning of the modern era, works of L.V. Kantorovich and G.B. Dantzig (so-called linear programming) can be considered amongst others. This book discusses a wide spectrum of optimization methods from classical to modern, alike heuristics. Novel as well as classical techniques is also discussed in this book, including its mutual intersection. Together with many interesting chapters, a reader will also encounter various methods used for proposed optimization approaches, such as game theory and evolutionary algorithms or modelling of evolutionary algorithm dynamics like complex networks. |
| dual problem linear programming: The Design of Competitive Online Algorithms Via a Primal-Dual Approach Niv Buchbinder, Joseph Naor, 2009 Extends the primal-dual method to the setting of online algorithms, and shows its applicability to a wide variety of fundamental problems. |
| dual problem linear programming: Linear Inequalities and Related Systems. (AM-38), Volume 38 Harold William Kuhn, Albert William Tucker, 2016-03-02 The description for this book, Linear Inequalities and Related Systems. (AM-38), Volume 38, will be forthcoming. |
| dual problem linear programming: Iterative Methods in Combinatorial Optimization Lap Chi Lau, R. Ravi, Mohit Singh, 2011-04-18 With the advent of approximation algorithms for NP-hard combinatorial optimization problems, several techniques from exact optimization such as the primal-dual method have proven their staying power and versatility. This book describes a simple and powerful method that is iterative in essence and similarly useful in a variety of settings for exact and approximate optimization. The authors highlight the commonality and uses of this method to prove a variety of classical polyhedral results on matchings, trees, matroids and flows. The presentation style is elementary enough to be accessible to anyone with exposure to basic linear algebra and graph theory, making the book suitable for introductory courses in combinatorial optimization at the upper undergraduate and beginning graduate levels. Discussions of advanced applications illustrate their potential for future application in research in approximation algorithms. |
| dual problem linear programming: Linear Programming and Network Flows Mokhtar S. Bazaraa, John J. Jarvis, Hanif D. Sherali, 1990 Table of contents |
| dual problem linear programming: Julia Programming for Operations Research Changhyun Kwon, 2019-03-03 Last Updated: December 2020 Based on Julia v1.3+ and JuMP v0.21+ The main motivation of writing this book was to help the author himself. He is a professor in the field of operations research, and his daily activities involve building models of mathematical optimization, developing algorithms for solving the problems, implementing those algorithms using computer programming languages, experimenting with data, etc. Three languages are involved: human language, mathematical language, and computer language. His team of students need to go over three different languages, which requires translation among the three languages. As this book was written to teach his research group how to translate, this book will also be useful for anyone who needs to learn how to translate in a similar situation. The Julia Language is as fast as C, as convenient as MATLAB, and as general as Python with a flexible algebraic modeling language for mathematical optimization problems. With the great support from Julia developers, especially the developers of the JuMP—Julia for Mathematical Programming—package, Julia makes a perfect tool for students and professionals in operations research and related areas such as industrial engineering, management science, transportation engineering, economics, and regional science. For more information, visit: http://www.chkwon.net/julia |
| dual problem linear programming: Theory of Linear and Integer Programming Alexander Schrijver, 1998-06-11 Theory of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis. It aims at complementing the more practically oriented books in this field. A special feature is the author's coverage of important recent developments in linear and integer programming. Applications to combinatorial optimization are given, and the author also includes extensive historical surveys and bibliographies. The book is intended for graduate students and researchers in operations research, mathematics and computer science. It will also be of interest to mathematical historians. Contents 1 Introduction and preliminaries; 2 Problems, algorithms, and complexity; 3 Linear algebra and complexity; 4 Theory of lattices and linear diophantine equations; 5 Algorithms for linear diophantine equations; 6 Diophantine approximation and basis reduction; 7 Fundamental concepts and results on polyhedra, linear inequalities, and linear programming; 8 The structure of polyhedra; 9 Polarity, and blocking and anti-blocking polyhedra; 10 Sizes and the theoretical complexity of linear inequalities and linear programming; 11 The simplex method; 12 Primal-dual, elimination, and relaxation methods; 13 Khachiyan's method for linear programming; 14 The ellipsoid method for polyhedra more generally; 15 Further polynomiality results in linear programming; 16 Introduction to integer linear programming; 17 Estimates in integer linear programming; 18 The complexity of integer linear programming; 19 Totally unimodular matrices: fundamental properties and examples; 20 Recognizing total unimodularity; 21 Further theory related to total unimodularity; 22 Integral polyhedra and total dual integrality; 23 Cutting planes; 24 Further methods in integer linear programming; Historical and further notes on integer linear programming; References; Notation index; Author index; Subject index |
| dual problem linear programming: Linear Programming and Economic Analysis Robert Dorfman, Paul A. Samuelson, Robert M. Solow, 2012-10-10 Designed primarily for economists and those interested in management economics who are not necessarily accomplished mathematicians, this text offers a clear, concise exposition of the relationship of linear programming to standard economic analysis. The research and writing were supported by The RAND Corporation in the late 1950s. Linear programming has been one of the most important postwar developments in economic theory, but until publication of the present volume, no text offered a comprehensive treatment of the many facets of the relationship of linear programming to traditional economic theory. This book was the first to provide a wide-ranging survey of such important aspects of the topic as the interrelations between the celebrated von Neumann theory of games and linear programming, and the relationship between game theory and the traditional economic theories of duopoly and bilateral monopoly. Modern economists will especially appreciate the treatment of the connection between linear programming and modern welfare economics and the insights that linear programming gives into the determinateness of Walrasian equilibrium. The book also offers an excellent introduction to the important Leontief theory of input-output as well as extensive treatment of the problems of dynamic linear programming. Successfully used for three decades in graduate economics courses, this book stresses practical problems and specifies important concrete applications. |
| dual problem linear programming: The Simplex Method of Linear Programming F.A. Ficken, 2015-06-17 Originally published: New York: Holt, Rinehart and Winston, 1961. |
| dual problem linear programming: Introduction to Linear Optimization Dimitris Bertsimas, John N. Tsitsiklis, 1997-01-01 |
| dual problem linear programming: Linear Programming Robert J Vanderbei, 2007-10-23 This Third Edition introduces the latest theory and applications in optimization. It emphasizes constrained optimization, beginning with linear programming and then proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. You’ll discover a host of practical business applications as well as non-business applications. With its focus on solving practical problems, the book features free C programs to implement the major algorithms covered. The book’s accompanying website includes the C programs, JAVA tools, and new online instructional tools and exercises. |
| dual problem linear programming: The Design of Approximation Algorithms David P. Williamson, David B. Shmoys, 2011-04-26 Discrete optimization problems are everywhere, from traditional operations research planning problems, such as scheduling, facility location, and network design; to computer science problems in databases; to advertising issues in viral marketing. Yet most such problems are NP-hard. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first part of the book is devoted to a single algorithmic technique, which is then applied to several different problems. The second part revisits the techniques but offers more sophisticated treatments of them. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithms courses, the book will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems. |
| dual problem linear programming: Lectures on Modern Convex Optimization Aharon Ben-Tal, Arkadi Nemirovski, 2001-01-01 Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications. |
| dual problem linear programming: Combinatorial Optimization Alexander Schrijver, 2003-02-12 From the reviews: About 30 years ago, when I was a student, the first book on combinatorial optimization came out referred to as the Lawler simply. I think that now, with this volume Springer has landed a coup: The Schrijver. The box is offered for less than 90.- EURO, which to my opinion is one of the best deals after the introduction of this currency. OR-Spectrum |
Marvel Rivals Console/Controller Settings Guide 2025
Dec 27, 2024 · Aim Response Curve Type: Determines how your controller responds when you tilt your right analog stick. You have a choice between Dual-Zone (the new default Overwatch …
Best armour and augments for Dual Guns + Longsword build
Apr 18, 2025 · Tc did specifically mention blossom dance. And resistances aren't important when using ghost walker/factory, which I assume he is given the dual guns. Yup I want to abuse …
Conditions for Dual Ultimates? - Dragon Ball: Xenoverse 2
As long as the custom partner has the Dual Ultimate equipped, they will use it every so often and then you can do the input for the second part of the attack no matter what you have equipped. …
Can I dual wield? - The Elder Scrolls IV: Oblivion - GameFAQs
Sep 10, 2007 · At stage 25 of The Path of Dawn quest, it is scripted for no apparent reason for Martin Septim to have a Lesser Staff of Lightning removed from his inventory, even though, …
Character Creation - Icewind Dale: Enhanced Edition ... - GameFAQs
Apr 30, 2021 · For two-class combinations, dual-classing from Fighter is slightly better than multiclassing because dual-classing gives Grand Mastery, more HP and faster level gain. …
Resident Evil: Director's Cut Walkthrough & Guide - GameFAQs
Mar 24, 2024 · The Director's Cut is the first version of the original Resident Evil that I had played and the one I like best. While the Dual Shock edition that followed adds functionality to the …
Differences between original and Dual Shock versions?
My bad, in regards to the Ink Ribbons... to be really specific, in both modes of the original Director's Cut and in Arrange Mode in the Dual Shock version, you get 3 ribbons each pickup. …
Character Creation - Baldur's Gate: Enhanced Edition ... - GameFAQs
Apr 21, 2024 · Multiclass vs. Dual Class There is a subtle distinction between multiclass characters and dual-class characters. The idea of playing an A / B multiclass character (for …
Ideal build for Rush for the first playthrough
For me I'm just going for a dual-wield build. Probably a ninja if I can get the requirements for it down. I was BR25 at The Fallen on PC and I got Rush to Ninja about halfway through. Now …
Some suggestions after 20+ hours for those still struggling
Oct 26, 2024 · Dual Gunner (Tech): fire-infused attack; Quadrastrike (Tech): high-BP damage (perfect for United Attack) Heeled Sandals (Legs): allows you to use a special kick attack …
Marvel Rivals Console/Controller Settings Guide 2025
Dec 27, 2024 · Aim Response Curve Type: Determines how your controller responds when you tilt your right analog stick. You have a choice between Dual-Zone (the new default Overwatch …
Best armour and augments for Dual Guns + Longsword build
Apr 18, 2025 · Tc did specifically mention blossom dance. And resistances aren't important when using ghost walker/factory, which I assume he is given the dual guns. Yup I want to abuse …
Conditions for Dual Ultimates? - Dragon Ball: Xenoverse 2
As long as the custom partner has the Dual Ultimate equipped, they will use it every so often and then you can do the input for the second part of the attack no matter what you have equipped. …
Can I dual wield? - The Elder Scrolls IV: Oblivion - GameFAQs
Sep 10, 2007 · At stage 25 of The Path of Dawn quest, it is scripted for no apparent reason for Martin Septim to have a Lesser Staff of Lightning removed from his inventory, even though, …
Character Creation - Icewind Dale: Enhanced Edition ... - GameFAQs
Apr 30, 2021 · For two-class combinations, dual-classing from Fighter is slightly better than multiclassing because dual-classing gives Grand Mastery, more HP and faster level gain. …
Resident Evil: Director's Cut Walkthrough & Guide - GameFAQs
Mar 24, 2024 · The Director's Cut is the first version of the original Resident Evil that I had played and the one I like best. While the Dual Shock edition that followed adds functionality to the …
Differences between original and Dual Shock versions?
My bad, in regards to the Ink Ribbons... to be really specific, in both modes of the original Director's Cut and in Arrange Mode in the Dual Shock version, you get 3 ribbons each pickup. …
Character Creation - Baldur's Gate: Enhanced Edition ... - GameFAQs
Apr 21, 2024 · Multiclass vs. Dual Class There is a subtle distinction between multiclass characters and dual-class characters. The idea of playing an A / B multiclass character (for …
Ideal build for Rush for the first playthrough
For me I'm just going for a dual-wield build. Probably a ninja if I can get the requirements for it down. I was BR25 at The Fallen on PC and I got Rush to Ninja about halfway through. Now …
Some suggestions after 20+ hours for those still struggling
Oct 26, 2024 · Dual Gunner (Tech): fire-infused attack; Quadrastrike (Tech): high-BP damage (perfect for United Attack) Heeled Sandals (Legs): allows you to use a special kick attack …
