General iterative methods for equilibrium and constrained convex minimization problem

被引：12

作者：

Tian, Ming ^{[1
,2
]}

Liu, Lei ^{[1
]}

机构：

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

[2] Tianjin Key Lab Adv Signal Proc, Civil Aviat Univ China, Tianjin 300300, Peoples R China

来源：

OPTIMIZATION | 2014年 / 63卷 / 09期

关键词：

iterative algorithm; equilibrium problem; constrained convex minimization; variational inequality; FIXED-POINT PROBLEMS; VISCOSITY APPROXIMATION METHODS; NONEXPANSIVE-MAPPINGS; STRONG-CONVERGENCE; ALGORITHMS;

D O I：

10.1080/02331934.2012.713361

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 gradient-projection algorithm (GPA) plays an important role in solving constrained convex minimization problems. Based on Marino and Xu's method [G. Marino and H.-K. Xu, A general method for nonexpansive mappings in Hilbert space, J. Math. Anal. Appl. 318 (2006), pp. 43-52], we combine GPA and averaged mapping approach to propose implicit and explicit composite iterative algorithms for finding a common solution of an equilibrium and a constrained convex minimization problem for the first time in this article. Under suitable conditions, strong convergence theorems are obtained.

引用

页码：1367 / 1385

页数：19

共 50 条

[21] Regularized gradient-projection methods for equilibrium and constrained convex minimization problems [J].

Ming Tian ;

Li-Hua Huang .

Journal of Inequalities and Applications, 2013

[22] Regularized gradient-projection methods for the constrained convex minimization problem and the zero points of maximal monotone operator [J].

Ming Tian ;

Si-Wen Jiao .

Fixed Point Theory and Applications, 2015

[23] Regularized gradient-projection methods for finding the minimum-norm solution of the constrained convex minimization problem [J].

Tian, Ming ;

Zhang, Hui-Fang .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017,

[24] An iterative algorithm for approximating convex minimization problem [J].

Yao, Yonghong ;

Liou, Yeong-Cheng ;

Yao, Jen-Chih .

APPLIED MATHEMATICS AND COMPUTATION, 2007, 188 (01) :648-656

[25] Projection and contraction methods for constrained convex minimization problem and the zero points of maximal monotone operator [J].

Wu, Yujing ;

Shi, Luoyi .

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2017, 10 (02) :637-646

[26] Iterative Scheme for Finding Solutions of the General Split Feasibility Problem and the General Constrained Minimization Problems [J].

Kangtunyakarn, Atid .

FILOMAT, 2019, 33 (01) :233-243

[27] Approximation of Solutions to Constrained Convex Minimization Problem in Hilbert Spaces [J].

Shehu Y. .

Vietnam Journal of Mathematics, 2015, 43 (3) :515-523

[28] Strong convergence of projection methods for a countable family of nonexpansive mappings and applications to constrained convex minimization problems [J].

Naraghirad, Eskandar .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013,

[29] HYBRID ITERATIVE TECHNIQUES APPROACH TO A MINIMIZATION PROBLEM [J].

Zheng, Lu ;

Yin, Tzu-Chien .

UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2022, 84 (02) :13-22

[30] Generalized mixed equilibria, variational inequalities and constrained convex minimization [J].

Ceng, Lu-Chuan ;

Wen, Ching-Feng .

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2017, 10 (02) :789-804

← 1 2 3 4 5 →