An Introduction to Optimization - Chong and Zak.pdf

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An Introduction to Optimization

WILEY-INTERSCIENCE SERIES IN DISCRETE MATHEMATICS AND OPTIMIZATION ADVISORY EDITORS RONALD L. GRAHAM University of California at San Diego, U.S.A. JAN KAREL LENSTRA Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands JOEL H. SPENCER + A complete list of titles in this series appears at the end of this volume. Institute, New York, New York, U.S.A.

An Introduction to Optimization Second Edition EDWIN K. P. CHONG STANISLAW H. ZAK A Wiley-lnterscience Publication INC. New York / Chichester / Weinheim / Brisbane / Singapore / Toronto JOHN WILEY & SONS,

This text is printed on acid-free paper. @ Copyright © 2001 by John Wiley & Sons, Inc. All rights reserved. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4744. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, (212) 850-6011, fax (212) 850-6008, E-Mail: PERMREQ @ W1LEY.COM. For ordering and customer service, call 1-800-CALL-W1LEY. Library of Congress Cataloging in Publication Data is available. ISBN: 0-471-39126-3 Printed in the United States of America 1 0 9 8 7 6 5 4 3

To my wife, Yat-Yee, and my parents, Paul and Julienne Chong. Edwin K. P. Chong To JMJ, my wife, Mary Ann, and my parents, Janina and Konstanty Zak. Stanislaw H. Zak

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Contents xiii 1 1 3 4 5 5 10 14 16 19 21 21 22 vii Preface Part I Mathematical Review 1 Methods of Proof and Some Notation 1.1 Methods of Proof 1.2 Notation Exercises 2 Vector Spaces and Matrices 2.1 Real Vector Spaces 2.2 Rank of a Matrix 2.3 Linear Equations 2.4 Inner Products and Norms Exercises 3 Transformations 3.1 Linear Transformations 3.2 Eigenvalues and Eigenvectors

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