Vector Optimization Set-Valued and Variational Analysis
Vector optimization model has found many important applications in decision making problems such as those in economics theory, management science, and engineering design (since the introduction of the Pareto optimal solu tion in 1896). Typical examples o
- PDF / 12,074,005 Bytes
- 315 Pages / 439.372 x 666.136 pts Page_size
- 60 Downloads / 327 Views
541
Guang-ya Chen Xuexiang Huang Xiaoqi Yang
Vector Optimization Set-Valued and Variational Analysis
Springer
Authors Prof. Guang-ya Chen Institute of Systems Science Chinese Academy of Sciences 100080 Beijing, China e-mail: [email protected]
Prof. Xiaoqi Yang Department of Applied Mathematics The Hong Kong Polytechnic University Kowloon, Hong Kong e-mail: [email protected]
Prof. Xuexiang Huang Department of Mathematics and Computer Sciences Chongqing Normal University 400047 Chongqing, China e-mail: [email protected]
Library of Congress Control Number: 2005927420
ISSN 0075-8442 ISBN-10 3-540-21289-2 Springer Berlin Heidelberg New York ISBN-13 978-3-540-21289-8 Springer Berlin Heidelberg New York 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, re-use of illustrations, recitation, broadcasting, reproduction on microfilms 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-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com © Springer-Verlag Berlin Heidelberg 2005 Printed in Germany 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. Typesetting: Camera ready by author Cover design: Erich Kirchner, Heidelberg Printed on acid-free paper
42/3130Di
5 4 3 2 10
To Our Parents
Preface
Vector optimization model has found many important applications in decision making problems such as those in economics theory, management science, and engineering design (since the introduction of the Pareto optimal solution in 1896). Typical examples of vector optimization model include maximization/minimization of the objective pairs (time, cost), (benefit, cost), and (mean, variance) etc. Many practical equilibrium problems can be formulated as variational inequality problems, rather than optimization problems, unless further assumptions are imposed. The vector variational inequality was introduced by Giannessi (1980). Extensive research on its relations with vector optimization, the existence of a solution and duality theory has been pursued. The fundamental idea of the Ekeland's variational principle is to assign an optimization problem a slightly perturbed one having a unique solution which is at the same time an approximate solution of the original problem. This principle has been an important tool for nonlinear analysis and optimization theory. Along with the development of vector optimization and set-valued optimization, the vector variational principle introduced by Ne
Data Loading...
