Equilibrium Problems and Variational Models

✍ Scribed by Qamrul Hasan Ansari, Jen-Chih Yao (auth.), Patrizia Daniele, Franco Giannessi, Antonino Maugeri (eds.)

• Publisher: Springer US
• Year: 2003
• Tongue: English
• Leaves: 450
• Series: Nonconvex Optimization and Its Applications 68
• Edition: 1
• Category: Library

✦ Synopsis

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

Front Matter....Pages i-xiii
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 R 2 ....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

✦ Subjects

Optimization; Mathematical Modeling and Industrial Mathematics