Introduction to Applied Optimization
This text presents a multi-disciplined view of optimization, providing students and researchers with a thorough examination of algorithms, methods, and tools from diverse areas of optimization without
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Applied Optimization Volume 80 Series Editors:
Panos M. Pardalos University of Florida, U.S.A.
Donald W. Hearn University ofFlorida, U.S.A.
Introduction to Applied Optimization Urmila M. Diwekar Center for Uncertain Systems: Tools for Optimization & Management Department of Chemical Engineering, and Institute for Environmental Science & Policy University of Illinois at Chicago Chicago, IL
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Library of Congress Cataloging-in-PubUcation ClP info or: Title: Introduction to Applied Optimization Author: Urmila Diwekar ISBN 978-1-4757-3747-9 ISBN 978-1-4757-3745-5 (eBook) DOI 10.1007/978-1-4757-3745-5 Copyright © 2003 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 2003. Softcover reprint of the hardcover 1st edition 2003 All rights reserved. No part ofthis pUblication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photo-copying, microfilming, recording, or otherwise, without the prior written permission of the publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Permissions for books published in the USA: permj S S j on s@wkap com Permissions for books published in Europe: [email protected] Printed on acid-free paper.
To my parents Leela and Murlidhar Diwekar for teaching me to be optimistic and to dream. To my husband Sanjay loag for supporting my dreams and making them a reality and To my four year old niece Ananya whose innocence and charm provide optimism for the future.
CONTENTS
FOREWORD ACKNOWLEDGEMENTS 1 INTRODUCTION 1.1 Problem Formulation: A Cautionary Note . . . . . . . 1.2 Degrees of Freedom Analysis . . . . . . . . . . . . . . 1.3 Objective Function, Constraints, and Feasible Region 1.4 NumericaIOptimization..... 1.5 Types of Optimization Problems 1.6 Summary....... 2 LINEAR PROGRAMMING 2.1 The Simplex Method 2.2 Infeasible Solution 2.3 Unbounded Solution 2.4 Multiple Solutions 2.5 Sensitivity Analysis . . . 2.6 Other Methods . . . . . 2.7 Hazardous Waste Blending Problem as an LP . 2.8 Summary.............. 3 NONLINEAR PROGRAMMING 3.1 Convex and Concave Functions . 3.2 Unconstrained NLP . . . . . . . . 3.3 Necessary and Sufficient Conditions, and Constrained NLP 3.4 Sensitivity Analysis . . . . . . . . . . . 3.5 Numerical Methods. . . . . . . . . . . 3.6 Hazardous Waste Blending: An NLP . 3.7 Summary............... 4 DISCRETE OPTIMIZATION 4.1 Tree and Network Representation. 4.2 Branch and Bound for IP . . . . . . 4.3 Numerical Methods for IP, MILP, and MINLP . 4.4 Probabilistic Methods. . . . . . . . . . . . . . . 4.5 Hazardous Waste Blending: A Combinatorial Problem 4.5.1 The OA based MINLP Approach. . . . 4.5.2 The Two-stage Approach with SA-NLP 4.5.3 A Branch and Bound Procedure 4.6 Summary......................
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