Linear Optimization and Extensions
I was pleasantly surprised when I was asked by Springer-Verlag to prepare a second edition of this volume on Linear Optimization and Extensions, which - not exactly contrary to my personal expectations - has apparently been accepted reasonably weIl by the
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Algorithms and Combinatorics 12
Editorial Board R.L. Graham, Murray Hin B. Karte, Bann 1. Lavasz, Budapest A.Wigdersan, Jerusalem G.M. Ziegler, Berlin
Springer-Verlag Berlin Heidelberg GmbH
Manfred Padberg
Linear Optimization and Extensions Second, Revised and Expanded Edition
Springer
Manfred Padberg Leonard N. Stern School ofBusiness Statistics and Operations Research Department N ew York University 44 West 4th Street, Suite 868 NewYork, NY 10012 - 1126, USA e-mail: [email protected]
Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Pndberg, Manfred:
Linear optimization and extensions / Manfred Padberg. - 2., rev. and expanded ed. (A1goritbms and combinatorics ; 12)
ISBN 978-3-642-08511-6 ISBN 978-3-662-12273-0 (eBook) DOI 10.1007/978-3-662-12273-0
Mathematics Subject Classification (1991): 68R02, 60C05, 05C02 ISSN 0937-5511 ISBN 978-3-642-08511-6 This work is subject to copyright. All rights are reserved. 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 way. and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law ofSeptember 9. 1965. in its current version. and permission for use must always be obtained from Springer-VerlagBerlinHeidelbergGmbH.Violations are liable for prosecution und er the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1999 Originally published by Springer-Verlag Berlin Heidelberg NewYork in 1999 Softcover reprint ofthe hardcover 2nd edition 1999
Typesetting: Camera-ready copy produced from the author's output file SPIN 10721810 46/3143 - 5 432 1 0 - Printed on acid-free paper
Preface to the Second Edition
I was pleasantly surprised when I was asked by Springer-Verlag to prepare a second edition of this volume on Linear Optimization and Extensions, which - not exactly contrary to my personal expectations - has apparently been accepted reasonably weIl by the global optimization community. My objective in putting this book together was originally - and still is - to detail the major algorithmic ideas in linear optimization that have evolved in the past fifty years or so and that have changed the historical optimization "landscape" in substantial ways - both theoretically and computationally. While I may have overlooked the importance of some very recent developments - the work by Farid Alizadeh which generalizes linear programming to "sem i-definite" programming is perhaps a candidate for one of my omissions - I think that major new breakthraughs on those two fronts that interest me - theory and computation - have not occurred since this book was published originally. As a consequence I have restricted myself to a thorough re-working of the original manuscript with the goal of making it more readable. Of course, I have taken this opportunity to correct a few "Schönheitsfehler" of the firs
