Equilibrium Problems and Variational Models

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.

On Vector Quasi—Equilibrium Problems.- The Log-Quadratic Proximal Methodology in Convex Optimization Algorithms and Variational Inequalities.- The Continuum Model of Transportation Problem.- The Economic Model for Demand—Supply Problems.- Constrained Problems of Calculus of Variations Via Penalization Technique.- Variational Problems with Constraints Involving Higher—Order Derivatives.- On the strong solvability of a unilateral boundary value problem for Nonlinear Parabolic Operators in the Plane.- Solving a Special Class of Discrete Optimal Control Problems Via a Parallel Interior—Point Method.- Solving Large Scale Fixed Charge Network Flow Problems.- Variable Projection Methods for Large—Scale Quadratic Optimization in data Analysis Applications.- Strong solvability of boundary value problems in elasticity with Unilateral Constraints.- Time Dependent Variational Inequalities — Some Recent Trends.- On the Contractibility of the Efficient and Weakly Efficient Sets in R2.- Existence Theorems for a Class of Variational Inequalities and Applications to a Continuous Model of Transportation.- On Auxiliary Principle for Equilibrium Problems.- Multicriteria Spatial Price Networks: Statics and Dynamics.- Non regular data in unilateral variational problems.- Equilibrium Concepts in Transportation Networks: Generalized Wardrop Conditions and Variational Formulations.- Variational Geometry and Equilibrium.- On the Calculation of Equilibrium in Time Dependent Traffic Networks.- Mechanical Equilibrium and Equilibrium Systems.- False Numerical Convergence in Some Generalized Newton Methods.- Distance to the Solution Set of an Inequality with an Increasing Function.- Transportation Networks with Capacity Constraints.