Equilibrium Problems and Variational Models

Editors: P. Daniele, Franco Giannessi, A. Maugeri



The volume, devoted to variational analysis and its applications, collects selected and refereed contributions, which provide an outline of the field. The meeting of the title "Equilibrium Problems and Variational Models", which was held in Erice (Sicily) in the period June 23 - July 2 2000, was the occasion of the presentation of some of these papers; other results are a consequence of a fruitful and constructive atmosphere created during the meeting. New results, which enlarge the field of application of variational analysis, are presented in the book; they deal with the vectorial analysis, time dependent variational analysis, exact penalization, high order deriva- tives, geometric aspects, distance functions and log-quadratic proximal methodology. The new theoretical results allow one to improve in a remarkable way the study of significant problems arising from the applied sciences, as continuum model of transportation, unilateral problems, multicriteria spatial price models, network equilibrium problems and many others. As noted in the previous book "Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models", edited by F. Giannessi, A. Maugeri and P.M. Pardalos, Kluwer Academic Publishers, Vol. 58 (2001), the progress obtained by variational analysis has permitted to han- dle problems whose equilibrium conditions are not obtained by the mini- mization of a functional. These problems obey a more realistic equilibrium condition expressed by a generalized orthogonality (complementarity) con- dition, which enriches our knowledge of the equilibrium behaviour. Also this volume presents important examples of this formulation.

Table of contents (24 chapters)

On Vector Quasi—Equilibrium Problems
Pages 1-18

The Log—Quadratic Proximal Methodology in Convex Optimization Algorithms and Variational Inequalities
Pages 19-52

The Continuum Model of Transportation Problem
Pages 53-60

The Economic Model for Demand—Supply Markets
Pages 61-78

Constrained Problems of Calculus of Variations Via Penalization Technique
Pages 79-108

Variational Problems with Constraints Involving Higher-Order Derivatives
Pages 109-134

On the Strong Solvability of a Unilateral Boundary Value Problem for Nonlinear Parabolic Operators in the Plane
Pages 135-140

Solving a Special Class of Discrete Optimal Control Problems Via a Parallel Interior—Point Method
Pages 141-161

Solving Large Scale Fixed Charge Network Flow Problems
Pages 163-183

Variable Projection Methods for Large—Scale Quadratic Optimization in Data Analysis Applications
Pages 185-211

Strong Solvability of Boundary Value Problems in Elasticity with Unilateral Constraints
Pages 213-224

Time Dependent Variational Inequalities — Some Recent Trends
Pages 225-264

On the Contractibility of the Efficient and Weakly Efficient Sets in
Pages 265-279

Existence Theorems for a Class of Variational Inequalities and Applications to a Continuous Model of Transportation
Pages 281-287

On Auxiliary Principle for Equilibrium Problems
Pages 289-298

Multicriteria Spatial Price Networks: Statics and Dynamics
Pages 299-321

Non Regular Data in Unilateral Variational Problems
Pages 323-332

Equilibrium Concepts in Transportation Networks: Generalized Wardrop Conditions and Variational Formulations
Pages 333-346

Variational Geometry and Equilibrium
Pages 347-368

On the Calculation of Equilibrium in Time Dependent Traffic Networks
Pages 369-377

Mechanical Equilibrium and Equilibrium Systems
Pages 379-399

False Numerical Convergence in Some Generalized Newton Methods
Pages 401-416

Distance to the Solution Set of an Inequality with an Increasing Function
Pages 417-431

Transportation Networks with Capacity Constraints
Pages 433-445