Differential and sensitivity properties of gap functions for vector variational inequalities

Abstract. The purpose of this paper is to investigate differential properties of a class of set-valued maps and gap functions involving vector variational inequalities. Relationship between their contingent derivatives are discussed. A formula computing contingent derivative of the gap functions is established. Optimality conditions of solutions for vector variational inequalities are obtained.

[1]  Kok Lay Teo,et al.  On the Stability of Generalized Vector Quasivariational Inequality Problems , 2002 .

[2]  Xiaoqi Yang,et al.  On the Gap Functions of Prevariational Inequalities , 2003 .

[3]  N. Xiu,et al.  The Dual Gap Function for Variational Inequalities , 2003 .

[4]  Jen-Chih Yao,et al.  On the Generalized Vector Variational Inequality Problem , 1997 .

[5]  F. Giannessi.  On Minty Variational Principle , 1998 .

[6]  C. J. Goh,et al.  Vector equilibrium problem and vector optimization , 1999, Eur. J. Oper. Res..

[7]  S. J. Li,et al.  Minimax Theorems for Set-Valued Mappings , 2000 .

[8]  J. Dauer,et al.  A Characterization of Proper Minimal Points as Solutions of Sublinear Optimization Problems , 1993 .

[9]  Tetsuzo Tanino,et al.  Stability and Sensitivity Analysis in Convex Vector Optimization , 1988 .

[10]  T. Tanino,et al.  Sensitivity analysis in multiobjective optimization , 1988 .

[11]  X. Q. Yang,et al.  Vector network equilibrium problems and nonlinear scalarization methods , 1999, Math. Methods Oper. Res..

[12]  D. Shi,et al.  Contingent derivative of the perturbation map in multiobjective optimization , 1991 .

[13]  Xiaoqi Yang,et al.  On Gap Functions for Vector Variational Inequalities , 2000 .

[14]  Giandomenico Mastroeni,et al.  On Minty Vector Variational Inequality , 2000 .

[15]  S. J. Li,et al.  Existence of solutions for a generalized vector quasivariational inequality , 1996 .

[16]  Xiaoqi Yang,et al.  Gap Functions and Existence of Solutions to Set-Valued Vector Variational Inequalities , 2002 .

[17]  Patrick T. Harker,et al.  Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications , 1990, Math. Program..

[18]  Patrice Marcotte,et al.  Erratum: Weak Sharp Solutions of Variational Inequalities , 2000, SIAM J. Optim..

[19]  N. D. Yen,et al.  Vector variational inequality as a tool for studying vector optimization problems , 1998 .

[20]  J. Aubin,et al.  Applied Nonlinear Analysis , 1984 .

[21]  G. Chen.  Existence of solutions for a vector variational inequality: An extension of the Hartmann-Stampacchia theorem , 1992 .