Accelerated hybrid and shrinking projection methods for variational inequality problems

被引：13

作者：

Thong Duong Viet ^{[1
]}

Nguyen The Vinh ^{[2
]}

Dang Van Hieu ^{[3
]}

机构：

[1] Natl Econ Univ, Fac Econ Math, Hanoi, Vietnam

[2] Univ Transport & Commun, Dept Math, Hanoi, Vietnam

[3] Ton Duc Thang Univ, Fac Math & Stat, Appl Anal Res Grp, Ho Chi Minh City, Vietnam

来源：

OPTIMIZATION | 2019年 / 68卷 / 05期

关键词：

Variational inequality problem; subgradient extragradient method; inertial method; Tseng's extragradient method; hybrid projection method; shrinking projection method; STRONG-CONVERGENCE THEOREMS; SUBGRADIENT EXTRAGRADIENT METHOD; FIXED-POINT PROBLEMS; NONEXPANSIVE-MAPPINGS; MONOTONE-OPERATORS; GRADIENT METHODS; ALGORITHM; WEAK;

D O I：

10.1080/02331934.2019.1566825

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：

In this paper, we introduce several new extragradient-like approximation methods for solving variational inequalities in Hilbert spaces. Our algorithms are based on Tseng's extragradient method, subgradient extragradient method, inertial method, hybrid projection method and shrinking projection method. Strong convergence theorems are established under appropriate conditions. Our results extend and improve some related results in the literature. In addition, the efficiency of our algorithms is shown through numerical examples which are defined by the hybrid projection methods.

引用

收藏

页码：981 / 998

页数：18

相关论文

共 46 条

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

Alvarez, F ;

Attouch, H .

SET-VALUED ANALYSIS, 2001, 9 (1-2) :3-11

[2] The heavy ball with friction method, I. The continuous dynamical system: Global exploration of the local minima of a real-valued function by asymptotic analysis of a dissipative dynamical system [J].

Attouch, H ;

Goudou, X ;

Redont, P .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2000, 2 (01) :1-34

[3] Asymptotic control and stabilization of nonlinear oscillators with non-isolated equilibria [J].

Attouch, H ;

Czarnecki, MO .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2002, 179 (01) :278-310

[4] Gradient-type penalty method with inertial effects for solving constrained convex optimization problems with smooth data [J].

Bot, Radu Ioan ;

Csetnek, Erno Robert ;

Nimana, Nimit .

OPTIMIZATION LETTERS, 2018, 12 (01) :17-33

[5] Strong convergence theorem by a hybrid extragradient-like approximation method for variational inequalities and fixed point problems [J].

Ceng, Lu-Chuan ;

Hadjisavvas, Nicolas ;

Wong, Ngai-Ching .

JOURNAL OF GLOBAL OPTIMIZATION, 2010, 46 (04) :635-646

[6] 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

[7] Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space [J].

Censor, Yair ;

Gibali, Aviv ;

Reich, Simeon .

OPTIMIZATION METHODS & SOFTWARE, 2011, 26 (4-5) :827-845

[8] Extensions of Korpelevich's extragradient method for the variational inequality problem in Euclidean space [J].

Censor, Yair ;

Gibali, Aviv ;

Reich, Simeon .

OPTIMIZATION, 2012, 61 (09) :1119-1132

[9] A GENERAL INERTIAL PROXIMAL POINT ALGORITHM FOR MIXED VARIATIONAL INEQUALITY PROBLEM [J].

Chen, Caihua ;

Ma, Shiqian ;

Yang, Junfeng .

SIAM JOURNAL ON OPTIMIZATION, 2015, 25 (04) :2120-2142

[10] Inertial projection and contraction algorithms for variational inequalities [J].

Dong, Q. L. ;

Cho, Y. J. ;

Zhong, L. L. ;

Rassias, Th. M. .

JOURNAL OF GLOBAL OPTIMIZATION, 2018, 70 (03) :687-704

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