Lecture Notes in Mathematics

By: George Isac

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Paperback | 14 December 1992

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304 Pages

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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 fundamental mathematics such as fixed point theory, ordered spaces, nonlinear analysis, topological degree, the study of variational inequalities and also with mathematical modeling and numerical analysis. Researchers and graduate students interested in mathematical modeling or nonlinear analysis will find here interesting and fascinating results.

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Calculus Geometry Optimisation Linear Programming Applied Mathematics Reference, Information & Interdisciplinary Subjects Research & Information Information theory Cybernetics & Systems Theory

Economics Economic Theory & Philosophy Business & Management Operational Research Management & Management Techniques Management Decision Making Econometrics

Introduction	p. 1
Preliminaries and Definitions of Principal Complementarity Problems	p. 4
Models and Applications	p. 16
Mathematical programming	p. 16
Game theory	p. 24
Variational inequalities and complementarity	p. 28
Mechanics and complementarity	p. 29
Maximizing oil production	p. 38
Complementarity problems in economics	p. 39
Equilibrium of traffic flows	p. 48
The linear complementarity problem and circuit simulation	p. 50
Complementarity and fixed point	p. 50
Equivalences	p. 52
Existence Theorems	p. 70
Boundedness of the solution set	p. 70
Feasibility and solvability	p. 87
General existence theorems	p. 116
The Order Complementarity Problem	p. 139
The linear order complementarity problem	p. 140
The generalized order complementarity problem	p. 146
The Implicit Complementarity Problem	p. 162
The implicit complementarity problem and the fixed point theory	p. 163
The implicit complementarity problem and a special variational inequality	p. 169
The implicit complementarity problem and coincidence equations on convex cones	p. 182
Isotone Projection Cones and Complementarity	p. 196
Isotone projection cones	p. 196
Isotone projection cones and the complementarity problem	p. 203
Mann's iterations and the complementarity problem	p. 212
Projective metrics and the complementarity problem	p. 214
Topics on Complementarity Problems	p. 220
The basic theorem of complementarity	p. 220
The multivalued order complementarity problem	p. 226
Some classes of matrices and the linear complementarity problem	p. 229
Some results about the cardinality of solution set	p. 237
Alternative theorems and complementarity problems	p. 244
Again on the implicit complementarity problem	p. 249
Some new complementarity problems	p. 256
Some special problems	p. 260
Bibliography	p. 270
Subject Index	p. 295
Table of Contents provided by Blackwell. All Rights Reserved.

Lecture Notes in Mathematics

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