Variational Inequalities and Network Equilibrium Problems

✍ Scribed by Antoni Carla (auth.), F. Giannessi, A. Maugeri (eds.)

• Publisher: Springer US
• Year: 1995
• Tongue: English
• Leaves: 304
• Edition: 1
• Category: Library

✦ Synopsis

This volume brings forth a set of papers presented at the conference on "Varia­ tional Inequalities and network equilibrium problems", held in Erice at the "G. Stam­ pacchia" School of the "E. Majorana" Centre for Scientific Culture in the period 19~25 June 1994. The meeting was conceived to contribute to the exchange between Variational Analysis and equilibrium problems, especially those related to network design. Most of the approaches and viewpoints of these fields are present in the volume, both as concerns the theory and the applications of equilibrium problems to transportation, computer and electric networks, to market behavior, and to bi~level programming. Being convinced of the great importance of equilibrium problems as well as of their complexity, the organizers hope that the merging of points of view coming from differ­ ent fields will stimulate theoretical research and applications. In this context Variational and Quasi~Variational Inequalities have shown them­ selves to be very important models for equilibrium problems. As a consequence in the last two decades they have received a lot of attention both as to mathematical inves­ tigation and applications. The proof that the above mentioned equilibrium problems can be expressed, in terms of Variational or Quasi~Variational Inequalities also in the non~standard and non~symmetric cases, has been a crucial improvement.

✦ Table of Contents

Front Matter....Pages i-xii
On a Separation Approach to Variational Inequalities....Pages 1-7
Traffic Scheduling in Telecommunication Systems and Network Flow....Pages 9-19
On the Duality Theory for Finite Dimensional Variational Inequalities....Pages 21-31
Some Properties of Periodic Solutions of Linear Control Systems via Quasi-Variational Inequalities....Pages 33-44
Generalized Quasi-Variational Inequalities and Traffic Equilibrium Problem....Pages 45-54
Vector Variational Inequality and Geometric Vector Optimization....Pages 55-67
Testing a New Class of Algorithms for Nonlinear Complementarity Problems....Pages 69-83
Equilibrium in Transport Networks with Capacity Constraints....Pages 85-100
Separation of Sets and Gap Functions for Quasi-Variational Inequalities....Pages 101-121
Stability of Monotone Variational Inequalities with Various Applications....Pages 123-142
A Primal-Dual Proximal Point Algorithm for Variational Inequality Problems....Pages 143-153
Relations between t —, s —, z —Domain Descriptions of Periodically—Switched Networks....Pages 155-168
On Side Constrained Models of Traffic Equilibria....Pages 169-178
Advantages and Drawbacks of Variational Inequalities Formulations....Pages 179-194
Variational and Quasi-Variational Inequalities in Network Flow Models. Recent Developments in Theory and Algorithms....Pages 195-211
A Variational Inequality Associated to a Scalar Conservation Law with Unilateral Constraints....Pages 213-223
Continuity of the Solution Set of Homogeneous Equilibrium Problems and Linear Complementarity Problems....Pages 225-234
Tensor Approximations of Smooth Nonlinear Complementarity Systems....Pages 235-249
Basic Existence Theorems for Generalized Variational and Quasi-Variational Inequalities....Pages 251-255
Sensitivity Analysis of Variational Inequalities by Normal-Map Techniques....Pages 257-269
Monotone Relations and Network Equilibrium....Pages 271-288
Generalized Monotonicity — Concepts and Uses....Pages 289-299
Back Matter....Pages 301-305

✦ Subjects

Social Work; Calculus of Variations and Optimal Control; Optimization; Mathematics, general; Mathematics of Computing