Equilibrium Problems

Nonsmooth Optimization and Variational Inequality Models

By: F. Giannessi, Franco Giannessi, Antonino Maugeri

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Hardcover | 31 January 2002

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320 Pages

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25.4 x 17.15 x 1.91

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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.

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Non-Fiction Science Science in General Mathematics Optimisation Game Theory Medicine Medicine in General Physics Calculus & Mathematical Analysis Calculus of Variations Linear Programming

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Published: 2nd December 2010

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Preface	p. xiii
On the numerical solution of finite-dimensional variational inequalities by an interior point method	p. 1
Introduction	p. 2
The IIPVI-method	p. 4
Algorithmic issues	p. 6
Numerical experiments	p. 11
Conclusions and perspectives	p. 20
References	p. 20
Fixed points in ordered Banach spaces and applications to elliptic boundary-value problems	p. 25
Introduction	p. 25
Fixed points of increasing functions	p. 26
Elliptic problems with discontinuous nonlinearities	p. 28
References	p. 31
A theorem of the alternative for linear control systems	p. 33
Introduction	p. 33
The proof of theorem 1.4	p. 37
References	p. 41
Variational inequalities for static equilibrium market. Lagrangean function and duality	p. 43
Introduction	p. 43
Proof of theorem 1.2	p. 48
Proof of theorem 1.3	p. 49
Calculation of the equilibrium	p. 53
Example	p. 55
References	p. 57
On dynamical equilibrium problems and variational inequalities	p. 59
Introduction	p. 60
A static market model	p. 60
The time-dependent market model	p. 64
Existence of equilibria	p. 67
References	p. 69
Nonlinear programming methods for solving optimal control problems	p. 71
Introduction	p. 72
Framework of the method	p. 74
Choice of the parameters	p. 77
A global algorithm	p. 82
Computational experience	p. 84
Optimal in-stream aeration	p. 84
Diffusion convection processes	p. 91
Numerical results	p. 96
References	p. 98
Optimal flow pattern in road networks	p. 101
Introduction	p. 101
The traditional theory of system optimization	p. 103
A new theory of optimal flow pattern	p. 107
Calculation of the optimal toll vector	p. 111
An application to the real case	p. 113
Conclusions	p. 116
References	p. 117
On the storng solvability of a unilateral boundary value problem for nolinear discontinuos operators in the plane	p. 119
Introduction	p. 120
Basic assumptions and main results	p. 121
Preliminary results	p. 122
Proof of the theorems	p. 123
References	p. 127
Most likely traffic equilibrium route flows analysis and computation	p. 129
Introduction	p. 130
Illustrative examples and applications	p. 130
Illustrative examples	p. 130
Applications	p. 131
Most likely equilibrium flows	p. 137
Preliminaries	p. 137
An alternative derivation	p. 139
Solution procedure for the entropy program	p. 141
Experimental results	p. 144
The Sioux Falls network	p. 146
The Winnipeg network	p. 147
The Linkoping network	p. 149
An application: Exhaust fume emission analysis	p. 151
Relation between the stochastic user equilibrium and the most likely route flows	p. 152
Relation between the models for finding the most likely O-D link flows and the most likely route flows	p. 153
References	p. 157
Existence of solutions to bilevel variational problems in Banach spaces	p. 161
Introduction	p. 161
A general existence result	p. 164
Monotone case	p. 166
Pseudomonotone case	p. 168
Open problems	p. 171
References	p. 172
On the existence of solutions to vector optimization problems	p. 175
Introduction	p. 175
Image space and separation	p. 176
Existence of a vector minimum point	p. 179
About the cone-compactness	p. 181
References	p. 184
Equilibrium problems and variational inequalities	p. 187
Introduction	p. 187
The Signorini problem	p. 188
The obstacle problem	p. 195
A continuous model of transportation	p. 198
References	p. 203
Axiomatization for approximate solutions in optimization	p. 207
Introduction	p. 207
Optimization problems	p. 210
Axioms	p. 211
Characterizations of solutions	p. 214
Vector optimization	p. 217
Approximation with sequences	p. 218
References	p. 220
Necessary and sufficient conditions of Wardrop type for vectorial traffic equilibria	p. 223
Introduction	p. 223
The scalar case	p. 224
The vectorial case	p. 225
Results	p. 226
References	p. 228
Approximate solutions and Tikhonov well-posedness for Nash equilibria	p. 231
Introduction	p. 231
T-wp for Nash equilibria	p. 233
A new approach to Tikhonov well-posedness for Nash equilibria	p. 235
Ordinality of T[superscript v]-wp	p. 237
Metric characterization of T[superscript v]-wp	p. 239
An application: oligopoly models	p. 241
Open problems	p. 243
References	p. 244
Equilibrium in time dependent traffic networks with delay	p. 247
Introduction	p. 247
The model	p. 249
Existence of Equilibria	p. 251
An example	p. 252
References	p. 253
New results on local minima and their applications	p. 255
References	p. 267
An overview on projection-type methods for convex large-scale quadratic programs	p. 269
Introduction	p. 270
The projection and splitting methods	p. 272
The variable projection method	p. 277
The adaptive variable projection method	p. 284
Updating rules for the projection parameter	p. 287
Solution of ineer QP subproblems	p. 289
Computational experiments	p. 291
References	p. 297
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Equilibrium Problems

Nonsmooth Optimization and Variational Inequality Models

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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Paperback

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