Duality in Vector Optimization
This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. After a preliminary chapter dedicated to convex analysis and minimality notions of sets with respect
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Vector Optimization The series in Vector Optimization contains publications in various fields of optimization with vector-valued objective functions, such as multiobjective optimization, multi criteria decision making, set optimization, vector-valued game theory and border areas to financial mathematics, biosystems, semidefinite programming and multiobjective control theory. Studies of continuous, discrete, combinatorial and stochastic multiobjective models in interesting fields of operations research are also included. The series covers mathematical theory, methods and applications in economics and engineering. These publications being written in English are primarily monographs and multiple author works containing current advances in these fields.
Radu Ioan Boţ
·
Sorin-Mihai Grad
·
Gert Wanka
Duality in Vector Optimization
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Dr. Radu Ioan Boţ Faculty of Mathematics Chemnitz University of Technology Reichenhainer Str. 39 09126 Chemnitz Germany [email protected]
Dr. Sorin-Mihai Grad Faculty of Mathematics Chemnitz University of Technology Reichenhainer Str. 39 09126 Chemnitz Germany [email protected]
Professor Dr. Gert Wanka Faculty of Mathematics Chemnitz University of Technology Reichenhainer Str. 39 09126 Chemnitz Germany [email protected]
e-ISSN 1867-898X ISSN 1867-8971 ISBN 978-3-642-02885-4 e-ISBN 978-3-642-02886-1 DOI 10.1007/978-3-642-02886-1 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009932674 © Springer-Verlag Berlin Heidelberg 2009 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, 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. Cover design: WMXDesign GmbH Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Radu Ioan Bot¸ dedicates this book to Cassandra and Nina Sorin-Mihai Grad dedicates this book to Carmen Lucia Gert Wanka dedicates this book to Johanna
Preface
The continuous and increasing interest concerning vector optimization perceptible in the research community, where contributions dealing with the theory of duality abound lately, constitutes the main motivation that led to writing this book. Decisive was also the research experience of the authors in this field, materialized in a number of wo
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