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Inequalities; Equalities; Implicit equalitites; Minimal representation; Existing theory; Implicit equalities; Redundant constraints; Minimal representation; Existing methods; Results from literature; Experimental results; Nonbinding constraints; Primal-dual relations; The simplex method; The complexity of linear programming; LP-equivalent problems; The ellipsoidal method.
During the Spring of 1979 one of us (Zionts) was invited to visit Erasmus University in Rotterdam, The Netherlands. It was there that Zionts met another of us (Telgen) who was then in the process of completing a dissertation on redundancy in linear programming. At that time, Telgen proposed an extended visit to Buffalo, during which time he and Zionts would do an extensive study on redundancy. Redundancy, hardly an exciting or new topic, does have numerous applications. Telgen and Zionts planned the project for the Summer of 1980, and enlisted the support of all the contributors as well as the other two members of our team (Karwan and Lotfi). Lotfi was then a Ph. D. student in Industrial Engineering searching for a thesis topic. Redundancy became his topic. Karwan and Zionts served as his thesis co-chairmen, with Telgen serving as an outside reader of the thesis. We initially had hoped to complete the study during Telgen's stay in Buffalo, but that was far too optimistic. Lotfi completed his dissertation during the late Spring-early Summer of 1981. As the project took shape, we decided that we had more than enough for an article, or even several articles. Accordingly, not wanting to produce redundant papers, we decided to produce this volume --- a state-of-the-art review of methods for handling redundancy and comprehensive tests of the various methods, together with extensions and further developments of the most promising methods.
This book offers a theoretical and computational presentation of a variety of linear programming algorithms and methods with an emphasis on the revised simplex method and its components. A theoretical background and mathematical formulation is included for each algorithm as well as comprehensive numerical examples and corresponding MATLAB® code. The MATLAB® implementations presented in this book are sophisticated and allow users to find solutions to large-scale benchmark linear programs. Each algorithm is followed by a computational study on benchmark problems that analyze the computational behavior of the presented algorithms. As a solid companion to existing algorithmic-specific literature, this book will be useful to researchers, scientists, mathematical programmers, and students with a basic knowledge of linear algebra and calculus. The clear presentation enables the reader to understand and utilize all components of simplex-type methods, such as presolve techniques, scaling techniques, pivoting rules, basis update methods, and sensitivity analysis.
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
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.
Search has been vital to artificial intelligence from the very beginning as a core technique in problem solving. The authors present a thorough overview of heuristic search with a balance of discussion between theoretical analysis and efficient implementation and application to real-world problems. Current developments in search such as pattern databases and search with efficient use of external memory and parallel processing units on main boards and graphics cards are detailed. Heuristic search as a problem solving tool is demonstrated in applications for puzzle solving, game playing, constraint satisfaction and machine learning. While no previous familiarity with heuristic search is necessary the reader should have a basic knowledge of algorithms, data structures, and calculus. Real-world case studies and chapter ending exercises help to create a full and realized picture of how search fits into the world of artificial intelligence and the one around us. Provides real-world success stories and case studies for heuristic search algorithms Includes many AI developments not yet covered in textbooks such as pattern databases, symbolic search, and parallel processing units
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.
This book on Operation Research has been specially written to meet the requirements of the M.Sc., M.Com. and M.B.A. students for all Indian Universities. The subject matter has been discussed in such a simple way that the students will find no difficulty to understand it. The proof of various theorems and examples has been given with minute details. Each chapter of this book contains complete theory and fairly large number of solved examples, sufficient problems have also been selected from various universities examination papers. Contents: Simulation, LPP with Applications, Minimization Problem, Replacement and Maintenance Theory.