Linear Programs and Related Problems

by Evar D. Nering, Albert W. Tucker

Overview

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.

Product Details

ISBN-13:	9780125154406
Publisher:	Elsevier Science
Publication date:	10/12/1992
Series:	Computer Science and Scientific Computing
Pages:	584
Product dimensions:	6.00(w) x 9.00(h) x (d)

About the Author

Evar D. Nering received his Ph.D. at Princeton University under the direction of Emil Artin. His early publications were in algebraic number theory and game theory. He was the author of two books on linear algebra, Linear Algebra and matrix Theory (John Wiley & Sons, 1963, 1970) and Elementary Linear Algebra (Saunders, 1973).His most recent activity has been in mathematical programming, including his collaboration with Albert W. Tucker since 1973. He was a faculty member at the University of Minnesota, The University of Arizona, and Arizona State University until his retirement in 1990. At Arizona State University he was Chairman of the Mathematics Department and a consultant to the faculty and staff on microcomputers.

The career of Albert W. Tucker spans more than 50 years at Princeton University. Best known today for his work in mathematical programming and game theory (e.g., the Kuhn-Tucker theorem, Tucker tableaux, and the Prisoner's Dilemma), he was also prominent in combinational topology in his earlier years. An outstanding teacher, leader, and editor, he has been Chairman of the Princeton Mathematics Department, President of the MAA, Chairman of the Mathematical Programming Society, and course instructor, thesis advisor, or general mentor to scores of active mathematicians. For many years before his retirement in 1974, he taught a popular junior-senior course in games and programs, the notes for which grew into this book-thanks to Evar D. Nering.

Table of Contents

Sample Linear Problems. Tableau Algebra. Canonical Duality. the Simplex Algorithm. General Linear Programs. Numerical Considerations. Matrix Games. Assignment and Matching Problems. Transportations Problems. Network Flow Problems. The Transshipment Problem. Nonlinear programs.

Editorial Reviews

Among the topics covered are duality, and max/min problems such as matrix games, network-flow and transshipment problems. Tableaux are introduced as graphical tools to assist in determining the next step, the feasibility, and the existence of optimal solutions. Exercises and questions follow each chapter; answers, many with explanation, are at the back of the book. Includes a PC disk containing programs and exercises for pivoting in tableaux and the Hungarian algorithm. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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