Topics in Nonconvex Optimization Theory and Applications
Nonconvex Optimization is a multi-disciplinary research field that deals with the characterization and computation of local/global minima/maxima of nonlinear, nonconvex, nonsmooth, discrete and continuous functions. Nonconvex optimization problems ar
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Shashi Kant Mishra Editor
Topics in Nonconvex Optimization Theory and Applications
1C
Editor Shashi Kant Mishra Banaras Hindu University Faculty of Science Dept. of Mathematics Varanasi India [email protected]
ISSN 1931-6828 ISBN 978-1-4419-9639-8 e-ISBN 978-1-4419-9640-4 DOI 10.1007/978-1-4419-9640-4 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011929034 © Springer Science+Business Media, LLC 2011 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. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
I would like to dedicate this volume to my teacher Prof. R. N. Mukherjee, who introduced this wonderful field of mathematics to me. I would also like to dedicate this volume to Prof. B. D. Craven who showed me the path in this research area.
Foreword
It is a great pleasure to learn that the Centre for Interdisciplinary Mathematical Sciences and the Department of Mathematics, Banaras Hindu University organized an Advanced Training Programme on Nonconvex Optimization and Its Applications. This programme was organized to introduce the subject to young researchers and college teachers working in the area of nonconvex optimization. During the five-day period several eminent professors from all over the country working in the area of optimization gave expository to advanced level lectures covering the following topics. (i) (ii) (iii) (iv) (v) (vi) (vii)
Quasi-convex optimization Vector optimization Penalty function methods in nonlinear programming Support vector machines and their applications Portfolio optimization Nonsmooth analysis Generalized convex optimization
Participants were given copies of the lectures. I understand from Dr. S. K. Mishra, the main organizer of the programme, that the participants thoroughly enjoyed the lectures related to nonconvex programming. I am sure the students will benefit greatly from this kind of training programme and I am confident that Dr. Mishra will conduct a more advanced programme of this kind soon. I also appreciate the efforts taken by him to get these lectures published by Springer. I am sure this volume will serve as excellent lecture notes in optimization for students and researchers working in this area. Chennai, April 2010
Thiruvenkatachari Parthasarathy
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