Parametric well-posedness for variational inequalities defined by bifunctions

被引：67

作者：

Fang, Ya-Ping ^{[1
]}

Hu, Rong

机构：

[1] Sichuan Univ, Dept Math, Chengdu, Sichuan, Peoples R China

[2] Chengdu Univ Informat Technol, Dept Computat Sci, Chengdu, Sichuan, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2007年 / 53卷 / 08期

基金：

中国国家自然科学基金;

关键词：

variational inequalities; Minty variational inequalities; parametric well-posedness; metric characterizations; bifunctions; OPTIMIZATION;

D O I：

10.1016/j.camwa.2006.09.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we introduce the concepts of parametric well-posedness for Stampacchia and Minty variational inequalities defined by bifunctions. We establish some metric characterizations of parametric well-posedness. Under suitable conditions, we prove that the parametric well-posedness is equivalent to the existence and uniqueness of solutions to these variational inequalities. (c) 2007 Elsevier Ltd. All rights reserved.

引用

页码：1306 / 1316

页数：11

共 23 条

[11]

Giannessi F, 1998, APPL OPTIMIZAT, V13, P93

[12] Extended well-posedness properties of vector optimization problems [J].

Huang, XX .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2000, 106 (01) :165-182

[13]

Kinderlehrer D., 1980, PURE APPL MATH, V88

[14] GENERALIZED MONOTONICITY AND GENERALIZED CONVEXITY [J].

KOMLOSI, S .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1995, 84 (02) :361-376

[15] Vector variational inequalities with cone-pseudomonotone bifunctions [J].

Lalitha, CS ;

Mehta, M .

OPTIMIZATION, 2005, 54 (03) :327-338

[16] Well-posedness and L-well-posedness for quasivariational inequalities [J].

Lignola, MB .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2006, 128 (01) :119-138

[17] Well-posedness for optimization problems with constraints defined by variational inequalities having a unique solution [J].

Lignola, MB ;

Morgan, J .

JOURNAL OF GLOBAL OPTIMIZATION, 2000, 16 (01) :57-67

[18] A CHARACTERIZATION OF THYHONOV WELL-POSEDNESS FOR MINIMUM PROBLEMS, WITH APPLICATIONS TO VARIATIONAL-INEQUALITIES [J].

LUCCHETTI, R ;

PATRONE, F .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1981, 3 (04) :461-476

[19] Characterizations of generalized convexities via generalized directional derivatives [J].

Sach, PH ;

Penot, JP .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1998, 19 (5-6) :615-634

[20]

Tykhonov A.N., 1966, J Comput Math Phys, V6, P631

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