Numerical Optimization.pdf

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Preface

THE AUDIENCE

EMPHASIS AND WRITING STYLE

TOPICS NOT COVERED

ADDITIONAL RESOURCE

ACKNOWLEDGMENTS

FINAL REMARK

Contents

Chapter 1

Introduction

Numerical Optimization Jorge Nocedal Stephen J. Wright Springer

Springer Series in Operations Research Editors: Peter Glynn Stephen M. Robinson Springer New York Berlin Heidelberg Barcelona Hong Kong London Milan Paris Singapore Tokyo

Jorge Nocedal Stephen J. Wright Numerical Optimization With 85 Illustrations 1 3

Jorge Nocedal ECE Department Northwestern University Evanston, IL 60208-3118 USA Stephen J. Wright Mathematics and Computer Science Division Argonne National Laboratory 9700 South Cass Avenue Argonne, IL 60439-4844 USA Series Editors: Peter Glynn Department of Operations Research Stanford University Stanford, CA 94305 USA Stephen M. Robinson Department of Industrial Engineering University of Wisconsin–Madison 1513 University Avenue Madison, WI 53706-1572 USA Cover illustration is from Pre-Hispanic Mexican Stamp Designs by Frederick V. Field, courtesy of Dover Publi- cations, Inc. Library of Congress Cataloging-in-Publication Data Nocedal, Jorge. Numerical optimization / Jorge Nocedal, Stephen J. Wright. p. cm. — (Springer series in operations research) Includes bibliographical references and index. ISBN 0-387-98793-2 (hardcover) 1. Mathematical optimization. I. Wright, Stephen J., 1960– . II. Title. QA402.5.N62 519.3—dc21 III. Series. 1999 99–13263 © 1999 Springer-Verlag New York, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identiﬁed, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. ISBN 0-387-98793-2 Springer-Verlag New York Berlin Heidelberg SPIN 10764949

To Our Parents: Ra´ul and Concepci´on Peter and Berenice

Preface This is a book for people interested in solving optimization problems. Because of the wide (and growing) use of optimization in science, engineering, economics, and industry, it is essential for students and practitioners alike to develop an understanding of optimization algorithms. Knowledge of the capabilities and limitations of these algorithms leads to a better understanding of their impact on various applications, and points the way to future research on improving and extending optimization algorithms and software. Our goal in this book is to give a comprehensive description of the most powerful, state-of-the-art, techniques for solving continuous optimization problems. By presenting the motivating ideas for each algorithm, we try to stimulate the reader’s intuition and make the technical details easier to follow. Formal mathematical requirements are kept to a minimum. Because of our focus on continuous problems, we have omitted discussion of important optimization topics such as discrete and stochastic optimization. However, there are a great many applications that can be formulated as continuous optimization problems; for instance, ﬁnding the optimal trajectory for an aircraft or a robot arm; identifying the seismic properties of a piece of the earth’s crust by ﬁtting a model of the region under study to a set of readings from a network of recording stations;

viii P r e f a c e designing a portfolio of investments to maximize expected return while maintaining an acceptable level of risk; controlling a chemical process or a mechanical device to optimize performance or meet standards of robustness; computing the optimal shape of an automobile or aircraft component. Every year optimization algorithms are being called on to handle problems that are much larger and complex than in the past. Accordingly, the book emphasizes large-scale optimization techniques, such as interior-point methods, inexact Newton methods, limited- memory methods, and the role of partially separable functions and automatic differentiation. It treats important topics such as trust-region methods and sequential quadratic program- ming more thoroughly than existing texts, and includes comprehensive discussion of such “core curriculum” topics as constrained optimization theory, Newton and quasi-Newton methods, nonlinear least squares and nonlinear equations, the simplex method, and penalty and barrier methods for nonlinear programming. THE AUDIENCE We intend that this book will be used in graduate-level courses in optimization, as of- fered in engineering, operations research, computer science, and mathematics departments. There is enough material here for a two-semester (or three-quarter) sequence of courses. We hope, too, that this book will be used by practitioners in engineering, basic science, and industry, and our presentation style is intended to facilitate self-study. Since the book treats a number of new algorithms and ideas that have not been described in earlier textbooks, we hope that this book will also be a useful reference for optimization researchers. Prerequisites for this book include some knowledge of linear algebra (including nu- merical linear algebra) and the standard sequence of calculus courses. To make the book as self-contained as possible, we have summarized much of the relevant material from these ar- eas in the Appendix. Our experience in teaching engineering students has shown us that the material is best assimilated when combined with computer programming projects in which the student gains a good feeling for the algorithms—their complexity, memory demands, and elegance—and for the applications. In most chapters we provide simple computer exercises that require only minimal programming proﬁciency. EMPHASIS AND WRITING STYLE We have used a conversational style to motivate the ideas and present the numerical algorithms. Rather than being as concise as possible, our aim is to make the discussion ﬂow in a natural way. As a result, the book is comparatively long, but we believe that it can be read relatively rapidly. The instructor can assign substantial reading assignments from the text and focus in class only on the main ideas.

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