Partial solution for an open question on pseudomonotone variational inequalities

被引：1

作者：

Pham Duy Khanh ^{[1
]}

机构：

[1] Univ Pedag Ho Chi Minh City, Dept Math, Ho Chi Minh City, Vietnam

来源：

APPLICABLE ANALYSIS | 2012年 / 91卷 / 09期

关键词：

variational inequality; Tikhonov regularization; small parameter; solution uniqueness; pseudomonotone operator; pseudoaffine operator; mean-value theorem for vector-valued functions;

D O I：

10.1080/00036811.2011.577743

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article gives a partial solution for the open question raised by Nguyen Thanh Hao [Tikhonov regularization algorithm for pseudomonotone variational inequalities, Acta Math. Vietnam., 31 (2006), 283-289] about uniqueness of the solution of the regularized problem VI(K, F-epsilon) of a pseudomonotone variational inequality VI(K, F) for sufficiently small parameter epsilon > 0. It is proved that, under certain additional assumptions, the desired solution uniqueness holds for some classes of pseudoaffine variational inequalities and pseudomonotone variational inequalities.

引用

页码：1691 / 1698

页数：8

共 9 条

[1] Bianchi M, 2003, J CONVEX ANAL, V10, P149
[2] Buckwalter J, 2002, MANY FACES OF OSTEOARTHRITIS, P3
[3] FACCHINEI F, 2003, FINITE DIMENSIONAL V, V1
[4] Facchinei Francisco., 2003, FINITE DIMENSIONAL V, V2, DOI DOI 10.1007/B97543
[5] AFFINE PSEUDOMONOTONE MAPPINGS AND THE LINEAR COMPLEMENTARITY-PROBLEM
GOWDA, MS
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1990, 11 (03) : 373 - 380
[6] Hao N.T., 2006, ACTA MATH VIETNAM, V31, P283
[7] Ioffe AD., 1979, THEORY EXTREMAL PROB
[8] On the solution existence of pseudomonotone variational inequalities
Kien, B. T.
Yao, J. -C.
Yen, N. D.
[J]. JOURNAL OF GLOBAL OPTIMIZATION, 2008, 41 (01) : 135 - 145
[9] Solution methods for pseudomonotone variational inequalities
N. N. Tam
Yao, J. C.
N. D. Yen
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2008, 138 (02) : 253 - 273

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