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Equilibrium Problems : Nonsmooth Optimization and Variational Inequality Models - F. Giannessi

Equilibrium Problems

Nonsmooth Optimization and Variational Inequality Models

By: F. Giannessi (Editor), A. Maugeri (Editor), Panos M. Pardalos (Editor)

Hardcover Published: 31st January 2002
ISBN: 9781402001611
Number Of Pages: 304

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The aim of the book is to cover the three fundamental aspects of research in equilibrium problems: the statement problem and its formulation using mainly variational methods, its theoretical solution by means of classical and new variational tools, the calculus of solutions and applications in concrete cases. The book shows how many equilibrium problems follow a general law (the so-called user equilibrium condition). Such law allows us to express the problem in terms of variational inequalities. Variational inequalities provide a powerful methodology, by which existence and calculation of the solution can be obtained.

Prefacep. xiii
On the numerical solution of finite-dimensional variational inequalities by an interior point methodp. 1
Introductionp. 2
The IIPVI-methodp. 4
Algorithmic issuesp. 6
Numerical experimentsp. 11
Conclusions and perspectivesp. 20
Referencesp. 20
Fixed points in ordered Banach spaces and applications to elliptic boundary-value problemsp. 25
Introductionp. 25
Fixed points of increasing functionsp. 26
Elliptic problems with discontinuous nonlinearitiesp. 28
Referencesp. 31
A theorem of the alternative for linear control systemsp. 33
Introductionp. 33
The proof of theorem 1.4p. 37
Referencesp. 41
Variational inequalities for static equilibrium market. Lagrangean function and dualityp. 43
Introductionp. 43
Proof of theorem 1.2p. 48
Proof of theorem 1.3p. 49
Calculation of the equilibriump. 53
Examplep. 55
Referencesp. 57
On dynamical equilibrium problems and variational inequalitiesp. 59
Introductionp. 60
A static market modelp. 60
The time-dependent market modelp. 64
Existence of equilibriap. 67
Referencesp. 69
Nonlinear programming methods for solving optimal control problemsp. 71
Introductionp. 72
Framework of the methodp. 74
Choice of the parametersp. 77
A global algorithmp. 82
Computational experiencep. 84
Optimal in-stream aerationp. 84
Diffusion convection processesp. 91
Numerical resultsp. 96
Referencesp. 98
Optimal flow pattern in road networksp. 101
Introductionp. 101
The traditional theory of system optimizationp. 103
A new theory of optimal flow patternp. 107
Calculation of the optimal toll vectorp. 111
An application to the real casep. 113
Conclusionsp. 116
Referencesp. 117
On the storng solvability of a unilateral boundary value problem for nolinear discontinuos operators in the planep. 119
Introductionp. 120
Basic assumptions and main resultsp. 121
Preliminary resultsp. 122
Proof of the theoremsp. 123
Referencesp. 127
Most likely traffic equilibrium route flows analysis and computationp. 129
Introductionp. 130
Illustrative examples and applicationsp. 130
Illustrative examplesp. 130
Applicationsp. 131
Most likely equilibrium flowsp. 137
Preliminariesp. 137
An alternative derivationp. 139
Solution procedure for the entropy programp. 141
Experimental resultsp. 144
The Sioux Falls networkp. 146
The Winnipeg networkp. 147
The Linkoping networkp. 149
An application: Exhaust fume emission analysisp. 151
Relation between the stochastic user equilibrium and the most likely route flowsp. 152
Relation between the models for finding the most likely O-D link flows and the most likely route flowsp. 153
Referencesp. 157
Existence of solutions to bilevel variational problems in Banach spacesp. 161
Introductionp. 161
A general existence resultp. 164
Monotone casep. 166
Pseudomonotone casep. 168
Open problemsp. 171
Referencesp. 172
On the existence of solutions to vector optimization problemsp. 175
Introductionp. 175
Image space and separationp. 176
Existence of a vector minimum pointp. 179
About the cone-compactnessp. 181
Referencesp. 184
Equilibrium problems and variational inequalitiesp. 187
Introductionp. 187
The Signorini problemp. 188
The obstacle problemp. 195
A continuous model of transportationp. 198
Referencesp. 203
Axiomatization for approximate solutions in optimizationp. 207
Introductionp. 207
Optimization problemsp. 210
Axiomsp. 211
Characterizations of solutionsp. 214
Vector optimizationp. 217
Approximation with sequencesp. 218
Referencesp. 220
Necessary and sufficient conditions of Wardrop type for vectorial traffic equilibriap. 223
Introductionp. 223
The scalar casep. 224
The vectorial casep. 225
Resultsp. 226
Referencesp. 228
Approximate solutions and Tikhonov well-posedness for Nash equilibriap. 231
Introductionp. 231
T-wp for Nash equilibriap. 233
A new approach to Tikhonov well-posedness for Nash equilibriap. 235
Ordinality of T[superscript v]-wpp. 237
Metric characterization of T[superscript v]-wpp. 239
An application: oligopoly modelsp. 241
Open problemsp. 243
Referencesp. 244
Equilibrium in time dependent traffic networks with delayp. 247
Introductionp. 247
The modelp. 249
Existence of Equilibriap. 251
An examplep. 252
Referencesp. 253
New results on local minima and their applicationsp. 255
Referencesp. 267
An overview on projection-type methods for convex large-scale quadratic programsp. 269
Introductionp. 270
The projection and splitting methodsp. 272
The variable projection methodp. 277
The adaptive variable projection methodp. 284
Updating rules for the projection parameterp. 287
Solution of ineer QP subproblemsp. 289
Computational experimentsp. 291
Referencesp. 297
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9781402001611
ISBN-10: 1402001614
Series: Nonconvex Optimization and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 304
Published: 31st January 2002
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 1.38