Introduction to Optimization Methods
During the last decade the techniques of non-linear optim ization have emerged as an important subject for study and research. The increasingly widespread application of optim ization has been stimulated by the availability of digital computers, and the
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CHAPMAN AND HALL MATHEMATICS SERIES
Edited by Professor R. Brown. Head of the Department of Pure Mathematics, University College of North Wales, Bangor, and Dr M.A.H. Dempster. University Lecturer in Industrial Mathematics and Fellow of Balliol College, Oxford A Preliminary Course in Analysis R.M.F. Moss and G.T. Roberts Elementary Differential Equations R.L.E. Schwarzenberger A First Course on Complex Functions G.J.O. Jameson Rings, Modules and Linear Algebra B. Hartley and T.O. Hawkes Regular Algebra and Finite Machines J.H. Conway Complex Numbers W.H. Cockcroft Galois Theory Ian Stewart Topology and Normed Spaces G.J.O. Jameson
Introduction to Optimization Methods P.R. ADB'Y Lecturer in Electrical Engineering University of London. King's College and
M.A.H. DEMPSTER University Lecturer in Industrial Mathematics and Fellow of Balliol College, Oxford
LONDON
CHAPMAN AND HALL
First published 1974 by Chapman and Hall Ltd 11 New Fetter Lane, London EC4P 4EE © 1974 P.R. Adby and M.A.H. Dempster
Set by E. W. C Wilkins Ltd, London and Northampton
ISBN-13: 978-0-412-11040-5 001: 10.1007/978-94-009-5705-3
e-ISBN-13: 978-94-009-5705-3
This limp-bound edition is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, re-sold, hired out, or otherwise circulated without the publisher's prior consent in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the subsequent purchaser. All rights reserved. No part of this book may be reprinted, or reproduced or utilized in any form or by any electronic, mechanical or other means, now known or hereafter invented, including photocopying and recording, or in any information storage and retrieval system, without permission in writing from the Publisher.
Distributed in the U.S.A. by Halsted Press, a Division of John Wiley & Sons, Inc. New York Library of Congress Catalog Card Number 74-4109
Preface
During the last decade the techniques of non-linear optimization have emerged as an important subject for study and research. The increasingly widespread application of optimization has been stimulated by the availability of digital computers, and the necessity of using them in the investigation of large systems. This book is an introduction to non-linear methods of
optimization and is suitable for undergraduate and postgraduate courses in mathematics, the physical and social sciences, and engineering. The first half of the book covers the basic optimization techniques including linear search methods, steepest descent, least squares, and the Newton-Raphson method. These are described in detail, with worked numerical examples, since they form the basis from which advanced methods are derived. Since 1965 advanced methods of unconstrained and constrained optimization have been developed to utilise the computational power of the digital computer. The second half of the book describes fully important algorithms in current use such as variable metric methods for
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