Generalizing Reduced Simplex Method
In Sects. 7.3–7.7, the general LP problem in form (7.11) was converted to the bounded-variable problem (7.13), and the latter was then solved by a generalized primal or dual simplex method. In this chapter, the primal and dual reduced simplex methods will
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Linear Programming Computation
Linear Programming Computation
Ping-Qi PAN
Linear Programming Computation
123
Ping-Qi PAN Department of Mathematics Southeast University Nanjing China
ISBN 978-3-642-40753-6 ISBN 978-3-642-40754-3 (eBook) DOI 10.1007/978-3-642-40754-3 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2013954780 © Springer-Verlag Berlin Heidelberg 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Dedicated to my parents, Chao Pan and Yiyun Yan and to my wife, Minghua Jiang, and my son, Yunpeng Pan
Preface
Linear programming (LP) (Dantzig 1948, 1951a,b,c) might be one of the most well-known and widely used mathematical tools in the world. As a branch of optimization, it serves as the most important cornerstone of operations research, decision science, and management science. This branch of study emerged when the American mathematician George B. Dantzig proposed the LP model and the simplex method in 1947. The computer, emerging around the same period, propelled the development of LP and the simplex method toward practical application. As a basic branch of study, LP orchestrated the birth of a number of new fields, such as nonlinear programming, network flow and combinatorial optimization, stochastic progra
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