Introduction to Nonsmooth Optimization Theory, Practice and Software
This book is the first easy-to-read text on nonsmooth optimization (NSO, not necessarily differentiable optimization). Solving these kinds of problems plays a critical role in many industrial applications and real-world modeling systems, for example in the
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ntroduction to Nonsmooth Optimization Theory, Practice and Software
Introduction to Nonsmooth Optimization
Adil Bagirov Napsu Karmitsa Marko M. Mäkelä •
Introduction to Nonsmooth Optimization Theory, Practice and Software
123
Adil Bagirov School of Information Technology and Mathematical Sciences, Centre for Informatics and Applied Optimization University of Ballarat Ballarat, VC Australia
ISBN 978-3-319-08113-7 DOI 10.1007/978-3-319-08114-4
Napsu Karmitsa Marko M. Mäkelä Department of Mathematics and Statistics University of Turku Turku Finland
ISBN 978-3-319-08114-4
(eBook)
Library of Congress Control Number: 2014943114 Springer Cham Heidelberg New York Dordrecht London Ó 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
Nonsmooth optimization refers to the general problem of minimizing (or maximizing) functions that are typically not differentiable at their minimizers (maximizers). These kinds of functions can be found in many applied fields, for example in image denoising, optimal control, neural network training, data mining, economics, and computational chemistry and physics. Since classical theory of optimization presumes certain differentiability and strong regularity assumptions for the
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