A class of gap functions for quasi-variational inequality problems

被引：48

作者：

Fukushima, Masao ^{[1
]}

机构：

[1] Kyoto Univ, Dept Appl Math & Phys, Grad Sch Informat, Kyoto 6068501, Japan

来源：

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION | 2007年 / 3卷 / 02期

关键词：

quasi-variational inequality problem; optimization reformulation; gap function;

D O I：

10.3934/jimo.2007.3.165

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We present a class of gap functions for the quasi-variational inequality problem (QVIP). We show the equivalence between the optimization reformulation with the gap function and the original QVIP. We also give conditions under which the gap function is continuous and directionally differentiable.

引用

页码：165 / 171

页数：7

共 18 条

[1]

Auslender A, 1976, Optimisation: Methodes numeques

[2] NASH POINTS IN CASE OF QUADRATIC FUNCTIONALS AND N-PERSON LINEAR-DIFFERENTIAL GAMES [J].

BENSOUSSAN, A .

SIAM JOURNAL ON CONTROL, 1974, 12 (03) :460-499

[3]

Bonnans JF., 2013, PERTURBATION ANAL OP

[4] THE GENERALIZED QUASI-VARIATIONAL INEQUALITY PROBLEM [J].

CHAN, D ;

PANG, JS .

MATHEMATICS OF OPERATIONS RESEARCH, 1982, 7 (02) :211-222

[5]

FACCHINEI F, 2006, GEN NASH EQUILIBRIUM

[6]

Facchinei F, 2003, Finite-Dimensional Variational Inequalities and Complementary Problems, VII

[7] EQUIVALENT DIFFERENTIABLE OPTIMIZATION PROBLEMS AND DESCENT METHODS FOR ASYMMETRIC VARIATIONAL INEQUALITY PROBLEMS [J].

FUKUSHIMA, M .

MATHEMATICAL PROGRAMMING, 1992, 53 (01) :99-110

[8]

GAINNESSI F, 1995, VARIATIONAL INEQUALI, P101

[9] GENERALIZED NASH GAMES AND QUASI-VARIATIONAL INEQUALITIES [J].

HARKER, PT .

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 1991, 54 (01) :81-94

[10] DIRECTIONAL DERIVATIVES FOR EXTREMAL-VALUE FUNCTIONS WITH APPLICATIONS TO COMPLETELY CONVEX CASE [J].

HOGAN, W .

OPERATIONS RESEARCH, 1973, 21 (01) :188-209

← 1 2 →