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E-raamat: Equilibrium Problems and Variational Models

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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 QuasiEquilibrium Problems.- The Log-Quadratic Proximal
Methodology in Convex Optimization Algorithms and Variational Inequalities.-
The Continuum Model of Transportation Problem.- The Economic Model for
DemandSupply Problems.- Constrained Problems of Calculus of Variations Via
Penalization Technique.- Variational Problems with Constraints Involving
HigherOrder 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
InteriorPoint Method.- Solving Large Scale Fixed Charge Network Flow
Problems.- Variable Projection Methods for LargeScale 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.