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Equilibrium Problems Nonsmooth Optimization and Variational Inequalities Models

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ISBN-10: 1402001614

ISBN-13: 9781402001611

Edition: 2001

Authors: Franco Giannessi, A. Maugeri, Panos M. Pardalos

List price: $169.99
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Description:

The aim of this book is to cover the three fundamental aspects of research in equilibrium problems. It shows how many equilibrium problems follow a general law, allowing us to express the problem in terms of variational inequalities.
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Book details

List price: $169.99
Copyright year: 2001
Publisher: Springer
Publication date: 1/31/2002
Binding: Hardcover
Pages: 304
Size: 6.75" wide x 10.00" long x 0.75" tall
Weight: 1.386
Language: English

Preface
On the numerical solution of finite-dimensional variational inequalities by an interior point method
Introduction
The IIPVI-method
Algorithmic issues
Numerical experiments
Conclusions and perspectives
References
Fixed points in ordered Banach spaces and applications to elliptic boundary-value problems
Introduction
Fixed points of increasing functions
Elliptic problems with discontinuous nonlinearities
References
A theorem of the alternative for linear control systems
Introduction
The proof of theorem 1.4
References
Variational inequalities for static equilibrium market. Lagrangean function and duality
Introduction
Proof of theorem 1.2
Proof of theorem 1.3
Calculation of the equilibrium
Example
References
On dynamical equilibrium problems and variational inequalities
Introduction
A static market model
The time-dependent market model
Existence of equilibria
References
Nonlinear programming methods for solving optimal control problems
Introduction
Framework of the method
Choice of the parameters
A global algorithm
Computational experience
Optimal in-stream aeration
Diffusion convection processes
Numerical results
References
Optimal flow pattern in road networks
Introduction
The traditional theory of system optimization
A new theory of optimal flow pattern
Calculation of the optimal toll vector
An application to the real case
Conclusions
References
On the storng solvability of a unilateral boundary value problem for nolinear discontinuos operators in the plane
Introduction
Basic assumptions and main results
Preliminary results
Proof of the theorems
References
Most likely traffic equilibrium route flows analysis and computation
Introduction
Illustrative examples and applications
Illustrative examples
Applications
Most likely equilibrium flows
Preliminaries
An alternative derivation
Solution procedure for the entropy program
Experimental results
The Sioux Falls network
The Winnipeg network
The Linkoping network
An application: Exhaust fume emission analysis
Relation between the stochastic user equilibrium and the most likely route flows
Relation between the models for finding the most likely O-D link flows and the most likely route flows
References
Existence of solutions to bilevel variational problems in Banach spaces
Introduction
A general existence result
Monotone case
Pseudomonotone case
Open problems
References
On the existence of solutions to vector optimization problems
Introduction
Image space and separation
Existence of a vector minimum point
About the cone-compactness
References
Equilibrium problems and variational inequalities
Introduction
The Signorini problem
The obstacle problem
A continuous model of transportation
References
Axiomatization for approximate solutions in optimization
Introduction
Optimization problems
Axioms
Characterizations of solutions
Vector optimization
Approximation with sequences
References
Necessary and sufficient conditions of Wardrop type for vectorial traffic equilibria
Introduction
The scalar case
The vectorial case
Results
References
Approximate solutions and Tikhonov well-posedness for Nash equilibria
Introduction
T-wp for Nash equilibria
A new approach to Tikhonov well-posedness for Nash equilibria
Ordinality of T[superscript v]-wp
Metric characterization of T[superscript v]-wp
An application: oligopoly models
Open problems
References
Equilibrium in time dependent traffic networks with delay
Introduction
The model
Existence of Equilibria
An example
References
New results on local minima and their applications
References
An overview on projection-type methods for convex large-scale quadratic programs
Introduction
The projection and splitting methods
The variable projection method
The adaptive variable projection method
Updating rules for the projection parameter
Solution of ineer QP subproblems
Computational experiments
References