The Existence of Maximum and Minimum Solutions to General Variational Inequalities in the Hilbert Lattices

被引：6

作者：

Li, Jinlu ^{[2
]}

Yao, Jen-Chih ^{[1
]}

机构：

[1] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan

[2] Shawnee State Univ, Dept Math, Portsmouth, OH 45662 USA

来源：

FIXED POINT THEORY AND APPLICATIONS | 2011年

关键词：

Variational Inequality; Convex Subset; Nonempty Subset; Banach Lattice; Minimum Solution;

D O I：

10.1155/2011/904320

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We apply the variational characterization of the metric projection to prove some results about the solvability of general variational inequalities and the existence of maximum and minimum solutions to some general variational inequalities in the Hilbert lattices.

引用

页数：19

共 14 条

[1]

[Anonymous], 1999, INDIAN J MATH

[2]

[Anonymous], 1998, Supermodularity and complementarity

[3]

[Anonymous], APPL MATH MECH

[4] ABSOLUTE NORMS ON VECTOR LATTICES [J].

BORWEIN, JM ;

YOST, DT .

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 1984, 27 (JUN) :215-222

[5] THE LINEAR ORDER COMPLEMENTARITY-PROBLEM [J].

BORWEIN, JM ;

DEMPSTER, MAH .

MATHEMATICS OF OPERATIONS RESEARCH, 1989, 14 (03) :534-558

[6] LEAST-ELEMENT THEORY OF SOLVING LINEAR COMPLEMENTARITY PROBLEMS AS LINEAR PROGRAMS. [J].

Cottle, Richard W. ;

Pang, Jong-Shi .

Mathematics of Operations Research, 1978, 3 (02) :155-170

[7] EQUIVALENCE OF LINEAR COMPLEMENTARITY-PROBLEMS AND LINEAR-PROGRAMS IN VECTOR LATTICE HILBERT-SPACES [J].

CRYER, CW ;

DEMPSTER, MAH .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1980, 18 (01) :76-90

[8]

ISAC G, 1992, LECT NOTES MATH, V1528, pR3

[9]

Isac G., 2001, NONLINEAR ANAL FORUM, V6, P383

[10]

NISHIMURA H, SOLVABILITY IN PRESS

← 1 2 →