Numerical approach to monotone variational inequalities by a one-step projected reflected gradient method with line-search procedure

被引：31

作者：

Mainge, Paul-Emile ^{[1
,2
]}

机构：

[1] Univ Antilles, DSI, Campus Schoelcher, Schoelcher 97233, Martinique, France

[2] FWI, LAMIA, Lamia, France

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2016年 / 72卷 / 03期

关键词：

Variational inequality; Projection method; Monotone operator; Projected reflected method; ALGORITHM;

D O I：

10.1016/j.camwa.2016.05.028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we revisit a recent approach to classical monotone variational inequalities by means of a projected reflected gradient-type method in R-N. A line-search procedure is incorporated for possible varying step-sizes and no Lipschitz-continuity condition on the operator is required. A main feature of the proposed method is that it requires only one projection step onto the feasible set at each iteration. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：720 / 728

页数：9

共 21 条

[1]

BERTSEKAS DP, 1982, MATH PROGRAM STUD, V17, P139

[2] GOLDSTEIN-LEVITIN-POLYAK GRADIENT PROJECTION METHOD [J].

BERTSEKAS, DP .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1976, 21 (02) :174-183

[3] An outer approximation method for the variational inequality problem [J].

Burachik, RS ;

Lopes, JO ;

Svaiter, BF .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2005, 43 (06) :2071-2088

[4] The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space [J].

Censor, Y. ;

Gibali, A. ;

Reich, S. .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2011, 148 (02) :318-335

[5]

Iusem A.N., 2000, Optimization, V48, P309

[6]

IUSEM AN, 1994, COMPUT APPL MATH, V13, P103

[7]

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

[8] MODIFICATION OF THE EXTRA-GRADIENT METHOD FOR SOLVING VARIATIONAL-INEQUALITIES AND CERTAIN OPTIMIZATION PROBLEMS [J].

KHOBOTOV, EN .

USSR COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 1987, 27 (9-10) :120-127

[9]

KORPELEVICH GM, 1976, EKONOMIKA MATEMATICH, V12, P747

[10]

Mainge P. E., 2015, INTERNAL REPORT

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