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E-raamat: Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models

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Equilibrium Problems: Nonsmooth Optimization and Variational Inequality ModelsSuurem pilt
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The aim of this book is to cover fundamental aspects of research on equilibrium problems. Treatment encompasses the statement of the problem and its formulation using mainly variational methods, the problem's theoretical solution by means of classic and new variational tools, the calculus of solutions, and applications. Many equilibrium problems, such as the Signorini problem, the obstacle problem, the discrete and continuous traffic equilibrium problem, and the spatial price equilibrium problem, are shown to follow a general law, the user equilibrium condition. Some of this material originated at a December 1998 conference held in Taormina. A subject index is missing. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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.
Preface xiii
On the numerical solution of finite-dimensional variational inequalities by an interior point method
1(24)
Stefanina Bellavia
Maria Grazia Gasparo
Introduction
2(2)
The IIPVI-method
4(2)
Algorithmic issues
6(5)
Numerical experiments
11(9)
Conclusions and perspectives
20(5)
References
20(5)
Fixed points in ordered Banach spaces and applications to elliptic boundary-value problems
25(8)
Gabriele Bonanno
Salvatore Marano
Introduction
25(1)
Fixed points of increasing functions
26(2)
Elliptic problems with discontinuous nonlinearities
28(5)
References
31(2)
A theorem of the alternative for linear control systems
33(10)
Paolo Cubiotti
Introduction
33(4)
The proof of theorem 1.4
37(6)
References
41(2)
Variational inequalities for static equilibrium market. Lagrangean function and duality
43(16)
Patrizia Daniele
Introduction
43(5)
Proof of theorem 1.2
48(1)
Proof of theorem 1.3
49(4)
Calculation of the equilibrium
53(2)
Example
55(4)
References
57(2)
On dynamical equilibrium problems and variational inequalities
59(12)
Patrizia Daniele
Antonino Maugeri
Introduction
60(1)
A static market model
60(4)
The time-dependent market model
64(3)
Existence of equilibria
67(4)
References
69(2)
Nonlinear programming methods for solving optimal control problems
71(30)
Carla Durazzi
Emanuele Galligani
Introduction
72(2)
Framework of the method
74(3)
Choice of the parameters
77(5)
A global algorithm
82(2)
Computational experience
84(17)
Optimal in-stream aeration
84(7)
Diffusion convection processes
91(5)
Numerical results
96(2)
References
98(3)
Optimal flow pattern in road networks
101(18)
Paolo Ferrari
Introduction
101(2)
The traditional theory of system optimization
103(4)
A new theory of optimal flow pattern
107(4)
Calculation of the optimal toll vector
111(2)
An application to the real case
113(3)
Conclusions
116(3)
References
117(2)
On the storng solvability of a unilateral boundary value problem for nolinear discontinuous operators in the plane
119(10)
Sofia Giuffre
Introduction
120(1)
Basic assumptions and main results
121(1)
Preliminary results
122(1)
Proof the theorems
123(4)
References
127(2)
Most likely traffic equilibrium route flows analysis and computation
129(32)
T. Larsson
J.T. Lundgren
M. Patriksson
C. Rydergren
Introduction
130(1)
Illustrative examples and applications
130(7)
Illustrative examples
130(1)
Applications
131(6)
Most likely equilibrium flows
137(4)
Preliminaries
137(2)
An alternative derivation
139(2)
Solution procedure for the entropy program
141(3)
Experimental results
144(7)
The Sioux Falls network
146(1)
The Winnipeg network
147(2)
The Linkoping network
149(2)
An application: Exhaust fume emission analysis
151(10)
Appendix A: Relation between the stochastic user equilibrium and the most likely route flows
152(1)
Appendix B: Relation between the models for finding the most likely O-D link flows and the most likely route flows
153(4)
References
157(4)
Existence of solutions to bilevel variational problems in Banach spaces
161(14)
Maria Beatrice Lignola
Jacqueline Morgan
Introduction
161(3)
A general existence result
164(2)
Monotone case
166(2)
Pseudomonotone case
168(3)
Open problems
171(4)
References
172(3)
On the existence of solutions to vector optimization problems
175(12)
Giandomenico Mastroeni
Massimo Pappalardo
Introduction
175(1)
Image space and separation
176(3)
Existence of a vector minimum point
179(2)
About the cone-compactness
181(6)
References
184(3)
Equilibrium problems and variational inequalities
187(20)
Antonino Maugeri
Introduction
187(1)
The Signorini problem
188(7)
The obstacle problem
195(3)
A continuous model of transportation
198(9)
References
203(4)
Axiomatization for approximate solutions in optimization
207(16)
Henk Norde
Fioravante Patrone
Introduction
207(3)
Optimization problems
210(1)
Axioms
211(3)
Characterizations of solutions
214(3)
Vector optimization
217(1)
Approximation with sequences
218(5)
References
220(3)
Necessary and sufficient conditions of Wardrop type for vectorial traffic equilibria
223(8)
Werner Oettli
Introduction
223(1)
The scalar case
224(1)
The vectorial case
225(1)
Results
226(5)
References
228(3)
Approximate solutions and Tikhonov well-posedness for Nash equilibria
231(16)
L. Pusillo Chicco
Introduction
231(2)
T-wp for Nash equilibria
233(2)
A new approach to Tikhonov well-posedness for Nash equilibria
235(2)
Ordinality of Tv-wp
237(2)
Metric characterization of Tv-wp
239(2)
An application: oligopoly models
241(2)
Open problems
243(4)
References
244(3)
Equilibrium in time dependent traffic networks with delay
247(8)
Fabio Raciti
Introduction
247(2)
The model
249(2)
Existence of Equilibria
251(1)
An example
252(3)
References
253(2)
New results on local minima and their applications
255(14)
Biagio Ricceri
References
267(2)
An overview on projection-type methods for convex largescale quadratic programs
269
Valeria Ruggiero
Luca Zanni
Introduction
270
The projection and splitting methods
272
The variable projection method
277
The adaptive variable projection method
284
Updating rules for the projection parameter
287
Solution of ineer QP subproblems
289
Computational experiments
291
References
297


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