Variational Inequalities and Network Equilibrium Problems / Edition 1

by F. Giannessi, A. Maugeri

Overview

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 different 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.

Product Details

ISBN-13:	9780306450075
Publisher:	Springer US
Publication date:	03/31/1995
Series:	Language of Science Series
Edition description:	1995
Pages:	305
Product dimensions:	7.01(w) x 10.00(h) x 0.03(d)

Table of Contents

1. On a separation approach to variational inequalities.- 2. Traffic scheduling in telecommunication systems and network flow.- 3. On the duality theory for finite dimensional variational inequalities.- 4. Some properties of periodic solutions of linear control systems via quasi-variational inequalities.- 5. Generalized quasi-variational inequalities and traffic equilibrium problem.- 6. Vector variational inequality and geometric vector optimization.- 7. Testing a new class of algorithms for nonlinear complementarity problems.- 8. Equilibrium in transport networks with capacity constraints.- 9. Separation of sets and gap functions for quasi-variational inequalities.- 10. Stability of monotone variational inequalities with various applications.- 11. A primal-dual proximal point algorithm for variational inequality problems.- 12. Relations between t—, s—, z—domain descriptions of periodically—switched networks.- 13. On side constrained models of traffic equilibria.- 14. Advantages and drawbacks of variational inequalities formulations.- 15. Variational and quasi-variational inequalities in network flow models. Recent developments in theory and algorithms.- 16. A variational inequality associated to a scalar conservation law with unilateral con straints.- 17. Continuity of the solution set of homogeneous equilibrium problems and linear complementarity problems.- 18. Tensor approximations of smooth nonlinear complementarity systems.- 19. Basic existence theorems for generalized variational and quasi-variational inequalities.- 20. Sensitivity analysis of variational inequalities by normal-map techniques.- 21. Monotone relations and network equilibrium.- 22. Generalized monotonicity—concepts and uses.- Contributors.

Editorial Reviews

An exchange between variational analysis and equilibrium studies as the two fields relate to network design, considering the theory and applications of equilibrium problems to transportation, computer and electric networks, market behavior, and bi-level programming. The 22 papers, from an international mathematics course in Erice, Italy, June 1994, include treatments of traffic scheduling in telecommunication systems and network flow, testing a new class of algorithms for nonlinear complementarity problems, the stability of monotone variational inequalities with various applications, and a variational inequality associated to a scalar conservation law with unilateral constraints. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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