Complementarity Problems
The study of complementarity problems is now an interesting mathematical subject with many applications in optimization, game theory, stochastic optimal control, engineering, economics etc. This subject has deep relations with important domains of fundame
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1528
Lecture Notes in Mathematics Editors: A. Dold, Heidelberg B. Eckmann, Zurich F. Takens, Groningen
1528
George Isac
Complementarity Problems
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest
Autor George Isac Departement de Mathematiques College Militaire Royal St. Jean Quebec, Canada J01 1RO
Mathematics Subject Classification (1991): 49A99, 58E35, 52A40
ISBN 3-540-56251-6 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-56251-6 Springer-Verlag New York Berlin Heidelberg 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-Verlag Berlin Heidelberg 1992 Printed in Germany Typesetting: Camera ready by author 46/3140-543210 - Printed on acid-free paper
TABLE OF CONTENTS
Introduction Chapter 1.
PRELIMINARIES AND DEFINITIONS OF PRINCIPAL COMPLEMENTARITY PROBLEMS
Chapter 2.
MODELS AND APPLICATIONS
4 16
2.1
Mathematical programming
16
2.2
Game theory
24
2.3
Variational inequalities and complementarity
28
2.4
Mechanics and complementarity
29
2.5
Maximizing oil production
38
2.6
Complementarity problems in economics
39
2.7
Equilibrium of traffic flows
48
2.8
The linear complementarity problem and circuit simulation
50
2.9
Complementarity and fixed point
50
Chapter 3.
EQUIVALENCES
52
Chapter 4.
EXISTENCE THEOREMS
70
4.1
Boundedness of the solution set
4.2
Feasibility and solvability
4.3
General existence theorems
Chapter 5.
70 87 116
THE ORDER COMPLEMENTARITY PROBLEM
139
5.1
The linear order complementarity problem
140
5.2
The generalized order complementarity problem
146
Chapter 6.
THE IMPLICIT COMPLEMENTARITY PROBLEM
162
6.1
The implicit complementarity problem and the fixed point theory
163
6.2
The implicit complementarity problem and a special variational
169
inequality 6.3
The implicit complementarity problem and coincidence equations on convex cones
182
VI
Chapter 7.
ISOTONE PROJECTION CONES AND COMPLEMENTARITY
196
Isotone projection cones
196
7.2
Isotone projection cones and the complementarity problem
203
7.3
Mann's iterations and the complementarity problem
212
7.4
Projective metrics and the complementarity problem
214
7.1
Chapter 8.
TOPICS ON COMPLEMENTARITY PROBLEMS
220
8.1
The basic theorem of complementarity
220
8.2
The multivalued order complementarity problem
226
8.3
Some classes of matrices and the linear complementarity problem
229
8.4
Some results about the cardinality of solution set
237
8.5
Alternative
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