Newton-Type Methods for Optimization and Variational Problems
This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for
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Alexey F. Izmailov Mikhail V. Solodov
Newton-Type Methods for Optimization and Variational Problems
Springer Series in Operations Research and Financial Engineering Series Editors: Thomas V. Mikosch Sidney I. Resnick Stephen M. Robinson
For further volumes: http://www.springer.com/series/3182
Alexey F. Izmailov • Mikhail V. Solodov
Newton-Type Methods for Optimization and Variational Problems
123
Alexey F. Izmailov Moscow State University Moscow, Russia
Mikhail V. Solodov Instituto de Matem´atica Pura e Aplicada Rio de Janeiro, Brazil
ISSN 1431-8598 ISSN 2197-1773 (electronic) ISBN 978-3-319-04246-6 ISBN 978-3-319-04247-3 (eBook) DOI 10.1007/978-3-319-04247-3 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2013958213 Mathematics Subject Classification (2010): 49-02, 90-02, 49M15, 49M37 © Springer International Publishing Switzerland 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
This book is entirely devoted to mathematical analysis of Newton-type methods for variational and optimization problems in finite-dimensional spaces. Newtonian methods are among the most important tools for solving problems of various kinds, in a variety of areas. Their value is impossible to overestimate. The general idea be
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