Vector Variational Inequalities and Vector Equilibria: Mathematical Theories

by F. Giannessi (Editor)

Overview

The book deals with the mathematical theory of vector variational ineq ualities with special reference to equilibrium problems. Such models h ave been introduced recently to study new problems from mechanics, str uctural engineering, networks, and industrial management, and to revis it old ones. The common feature of these problems is that given by the presence of concurrent objectives and by the difficulty of identifyin g a global functional (like energy) to be extremized. The vector varia tional inequalities have the advantage of both the variational ones an d vector optimization which are found as special cases. Among several applications, the equilibrium flows on a network receive special atten tion.

Product Details

ISBN-13:	9780792360261
Publisher:	Springer US
Publication date:	12/31/1999
Series:	Nonconvex Optimization and Its Applications , #38
Edition description:	2000
Pages:	526
Product dimensions:	6.14(w) x 9.21(h) x 0.36(d)

Table of Contents

Vector Equilibrium Problems and Vector Variational Inequalities.- Generalized Vector Variational-Like Inequalities and their Scalarization.- Existence of Solutions for Generalized Vector Variational-Like Inequalities.- On Gap Functions for Vector Variational Inequalities.- Existence of Solutions for Vector Variational Inequalities.- On the Existence of Solutions to Vector Complementarity Problems.- Vector Variational Inequalities and Modelling of a Continuum Traffic Equilibrium Problem.- Generalized Vector Variationa-Like Inequalities without Monotonicity.- Generalized Vector Variationa-Like Inequalities with Cx-?-Pseudomonotone Set-Valued Mappings.- A Vector Variationa-Like Inequality for Compact Acyclic Multifunctions and its Applications.- On the Theory of Vector Optimization and Variational Inequalities. Image Space Analysis and Separation.- Scalarization Methods for Vector Variational Inequality.- Super Efficiency for a Vector Equilibrium in Locally Convex Topological Vector Spaces.- The Existence of Essentially Connected Components of Solutions for Variational Inequalities.- Existence of Solutions for Vector Saddle-Point Problems.- Vector Variational Inequality as a Tool for Studying Vector Optimization Problems.- Vector Variational Inequalities in a Hausdorff Topological Vector Space.- Vector Ekeland Variational Principle.- Convergence of Approximate Solutions and Values in Parametric Vector Optimization.- On Minty Vector Variational Inequality.- Generalized Vector Variational-Like Inequalities.- On Vector Complementarity Systems and Vector Variational Inequalities.- Generalized Vector Variational Inequalities.- Vector Equilibrium Problems with Set-Valued Mappings.- On Some Equivalent Conditions of Vector Variational Inequalities.- On Inverse Vector VariationalInequalities.- Vector Variational Inequalities, Vector Equilibrium Flow and Vector Optimization.- On Monotone and Strongly Monotone Vector Variational Inequalities.- Connectedness and Stability of the Solution Sets in Linear Fractional Vector Optimization Problems.- Vector Variational Inequality and Implicit Vector Complementarity Problems.- References on Vector Variational Inequalities.- Contributors.