Korpelevich's method for variational inequality problems on Hadamard manifolds

被引：66

作者：

Tang, Guo-ji ^{[1
]}

Huang, Nan-jing ^{[1
]}

机构：

[1] Sichuan Univ, Dept Math, Chengdu 610064, Peoples R China

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2012年 / 54卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Extragradient method; Variational inequality; Hadamardmanifold; Pseudomonotone vector field; MONOTONE VECTOR-FIELDS; PROXIMAL POINT ALGORITHM; PROJECTION METHOD; CONVEX-FUNCTIONS; QUASI-CONVEX; SETS;

D O I：

10.1007/s10898-011-9773-3

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

The concept of pseudomonotone vector field on Hadamard manifold is introduced. A variant of Korpelevich's method for solving the variational inequality problem is extended from Euclidean spaces to constant curvature Hadamard manifolds. Under a pseudomonotone assumption on the underlying vector field, we prove that the sequence generated by the method converges to a solution of variational inequality, whenever it exists. Moreover, we give an example to show the effectiveness of our method.

引用

页码：493 / 509

页数：17

共 34 条

[11] Subgradient algorithm on Riemannian manifolds [J].

Ferreira, OP ;

Oliveira, PR .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1998, 97 (01) :93-104

[12]

Giannessi F., 2001, Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models

[13] Korpelevich's method for variational inequality problems in Banach spaces [J].

Iusem, Alfredo N. ;

Nasri, Mostafa .

JOURNAL OF GLOBAL OPTIMIZATION, 2011, 50 (01) :59-76

[14]

Iusem AN., 1997, OPTIMIZATION, V42, P309, DOI DOI 10.1080/02331939708844365

[15] COMPLEMENTARITY PROBLEMS OVER CONES WITH MONOTONE AND PSEUDOMONOTONE MAPS [J].

KARAMARDIAN, S .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1976, 18 (04) :445-454

[16]

Kinderlehrer D., 1980, An introduction to variational inequalities and their applications, V88

[17]

Korpelevich G. M., 1976, Ekon Mate Metody, V12, P747

[18] Resolvents of Set-Valued Monotone Vector Fields in Hadamard Manifolds [J].

Li, Chong ;

Lopez, Genaro ;

Martin-Marquez, Victoria ;

Wang, Jin-Hua .

SET-VALUED AND VARIATIONAL ANALYSIS, 2011, 19 (03) :361-383

[19]

Li C, 2010, TAIWAN J MATH, V14, P541

[20] Monotone vector fields and the proximal point algorithm on Hadamard manifolds [J].

Li, Chong ;

Lopez, Genaro ;

Martin-Marquez, Victoria .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2009, 79 :663-683

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