An efficient projection-type method for monotone variational inequalities in Hilbert spaces

被引：56

作者：

Shehu, Yekini ^{[1
,2
]}

Li, Xiao-Huan ^{[3
]}

Dong, Qiao-Li ^{[3
]}

机构：

[1] IST Austria, Campus 1, A-3400 Klosterneuburg, Austria

[2] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

[3] Civil Aviat Univ China, Coll Sci, Tianjin 300300, Peoples R China

来源：

NUMERICAL ALGORITHMS | 2020年 / 84卷 / 01期

关键词：

Variational inequality; Projection method; Inertial term; Strong convergence; Hilbert space; SUBGRADIENT EXTRAGRADIENT METHOD; STRONG-CONVERGENCE; GRADIENT METHODS; HYBRID METHOD; ALGORITHM; STEP; SEARCH; POINT;

D O I：

10.1007/s11075-019-00758-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the monotone variational inequality problem in a Hilbert space and describe a projection-type method with inertial terms under the following properties: (a) The method generates a strongly convergent iteration sequence; (b) The method requires, at each iteration, only one projection onto the feasible set and two evaluations of the operator; (c) The method is designed for variational inequality for which the underline operator is monotone and uniformly continuous; (d) The method includes an inertial term. The latter is also shown to speed up the convergence in our numerical results. A comparison with some related methods is given and indicates that the new method is promising.

引用

页码：365 / 388

页数：24

共 54 条

[1] An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping [J].