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Practical Optimization.pdf

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    PRACTICAL OPTIMIZATION Algorithms and Engineering Applications
    PRACTICAL OPTIMIZATION Algorithms and Engineering Applications Andreas Antoniou Wu-Sheng Lu Department of Electrical and Computer Engineering University of Victoria, Canada Spri inger
    Andreas Antoniou Department of ECE University of V ictoria British Columbia Canada aantoniou@shaw.ca Wu-Sheng Lu Department of ECE University of V ictoria British Columbia Canada wslu@ece.uvic,ca Library of Congress Control Number: 2007922511 Practical Optimization: Algorithms and Engineering Applications by Andreas Antoniou and Wu-Sheng Lu ISBN-10: 0-387-71106-6 ISBN-13: 978-0-387-71106-5 e-ISBN-10: 0-387-71107-4 e-ISBN-13: 978-0-387-71107-2 Printed on acid-free paper. © 2007 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, 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 in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. 9 8 7 6 5 4 3 2 1 springer.com
    To Lynne and Chi'Tang Catherine with our love
    About the authors: Andreas Antoniou received the Ph.D. degree in Electrical Engineering from the University of London, UK, in 1966 and is a Fellow of the lET and IEEE. He served as the founding Chair of the Department of Electrical and Computer Engineering at the University of Victoria, B.C., Canada, and is now Professor Emeritus in the same department. He is the author of Digital Filters: Analysis, Design, and Applications (McGraw-Hill, 1993) and Digital Signal Processing: Signals, Systems, and Filters (McGraw-Hill, 2005). He served as Associate Editor/Editor of IEEE Transactions on Circuits and Systems from June 1983 to May 1987, as a Distinguished Lecturer of the IEEE Signal Processing Society in 2003, as General Chair of the 2004 International Symposium on Circuits and Systems, and is currently serving as a Distinguished Lecturer of the IEEE Circuits and Systems Society. He received the Ambrose Fleming Premium for 1964 from the lEE (best paper award), the CAS Golden Jubilee Medal from the IEEE Circuits and Systems Society, the B.C. Science Council Chairman's Award for Career Achievement for 2000, the Doctor Honoris Causa degree from the Metsovio National Technical University of Athens, Greece, in 2002, and the IEEE Circuits and Systems Society 2005 Technical Achievement Award. Wu-Sheng Lu received the B.S. degree in Mathematics from Fudan University, Shanghai, China, in 1964, the M.E. degree in Automation from the East China Normal University, Shanghai, in 1981, the M.S. degree in Electrical Engineer ing and the Ph.D. degree in Control Science from the University of Minnesota, Minneapolis, in 1983 and 1984, respectively. He was a post-doctoral fellow at the University of Victoria, Victoria, BC, Canada, in 1985 and Visiting Assistant Professor with the University of Minnesota in 1986. Since 1987, he has been with the University of Victoria where he is Professor. His current teaching and research interests are in the general areas of digital signal processing and application of optimization methods. He is the co-author with A. Antoniou of Two-Dimensional Digital Filters (Marcel Dekker, 1992). He served as an As sociate Editor of the Canadian Journal of Electrical and Computer Engineering in 1989, and Editor of the same journal from 1990 to 1992. He served as an Associate Editor for the IEEE Transactions on Circuits and Systems, Part II, from 1993 to 1995 and for Part I of the same journal from 1999 to 2001 and from 2004 to 2005. Presently he is serving as Associate Editor for the Inter national Journal of Multidimensional Systems and Signal Processing. He is a Fellow of the Engineering Institute of Canada and the Institute of Electrical and Electronics Engineers.
    Dedication Biographies of the authors Preface Abbreviations 1. THE OPTIMIZATION PROBLEM Introduction 1.1 1.2 The Basic Optimization Problem 1.3 General Structure of Optimization Algorithms 1.4 Constraints 1.5 The Feasible Region 1.6 Branches of Mathematical Programming References Problems 2. BASIC PRINCIPLES Introduction 2.1 2.2 Gradient Information 2.3 The Taylor Series 2.4 Types of Extrema 2.5 Necessary and Sufficient Conditions for Local Minima and Maxima 2.6 Classification of Stationary Points 2.7 Convex and Concave Functions 2.8 Optimization of Convex Functions References Problems 3. GENERAL PROPERTIES OF ALGORITHMS Introduction 3.1 3.2 An Algorithm as a Point-to-Point Mapping 3.3 An Algorithm as a Point-to-Set Mapping 3.4 Closed Algorithms 3.5 Descent Functions 3.6 Global Convergence v vii xv xix 1 1 4 8 10 17 22 24 25 27 27 27 28 31 33 40 51 58 60 60 65 65 65 67 68 71 72
    3.7 Rates of Convergence References Problems 4. ONE-DIMENSIONAL OPTIMIZATION Introduction 4.1 4.2 Dichotomous Search 4.3 Fibonacci Search 4.4 Golden-Section Search 4.5 Quadratic Interpolation Method 4.6 Cubic Interpolation 4.7 The Algorithm of Davies, Swann, and Campey 4.8 Inexact Line Searches References Problems 5. BASIC MULTIDIMENSIONAL GRADIENT METHODS Introduction 5.1 5.2 Steepest-Descent Method 5.3 Newton Method 5.4 Gauss-Newton Method References Problems 6. CONJUGATE-DIRECTION METHODS Introduction 6.1 6.2 Conjugate Directions 6.3 Basic Conjugate-Directions Method 6.4 Conjugate-Gradient Method 6.5 Minimization of Nonquadratic Functions 6.6 Fletcher-Reeves Method 6.7 Powell's Method 6.8 Partan Method References 76 79 79 81 81 82 85 92 95 99 101 106 114 114 119 119 120 128 138 140 140 145 145 146 149 152 157 158 159 168 172
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