New projection methods for equilibrium problems over fixed point sets

被引：6

作者：

Anh, Pham Ngoc ^{[1
]}

Van Hong, Nguyen ^{[2
]}

机构：

[1] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam

[2] Haiphong Univ, Fac Math Educ, Haiphong, Vietnam

来源：

OPTIMIZATION LETTERS | 2021年 / 15卷 / 02期

关键词：

Equilibrium problem; Projection method; Fixed point; Subgradient; Demicontractive mapping; GENERALIZED MONOTONE BIFUNCTIONS; STRONG-CONVERGENCE THEOREM; ITERATIVE ALGORITHMS;

D O I：

10.1007/s11590-020-01625-9

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 some new approximation projection algorithms for solving monotone equilibrium problems over the intersection of fixed point sets of demicontractive mappings. By combining subgradient projection methods and hybrid steepest descent methods, strong convergence of the algorithms to a solution is shown in a real Hilbert space. Some numerical illustrations and comparisons are also reported to show the efficiency and advantage of the proposed algorithms.

引用

页码：627 / 648

页数：22

共 34 条

[1] On ergodic algorithms for equilibrium problems
Anh, P. N.
Hai, T. N.
Tuan, P. M.
[J]. JOURNAL OF GLOBAL OPTIMIZATION, 2016, 64 (01) : 179 - 195
[2] Subgradient projection methods extended to monotone bilevel equilibrium problems in Hilbert spaces
Anh, Pham Ngoc
Tu, Ho Phi
[J]. NUMERICAL ALGORITHMS, 2021, 86 (01) : 55 - 74
[3] A parallel subgradient method extended to variational inequalities involving nonexpansive mappings
Anh, Pham Ngoc
Hien, Nguyen Duc
Phuong, Ngo Xuan
Ngoc, Vu The
[J]. APPLICABLE ANALYSIS, 2020, 99 (16) : 2776 - 2792
[4] [Anonymous], 2001, INHERENTLY PARALLEL, DOI DOI 10.1016/S1570-579X(01)80028-8
[5] Generalized monotone bifunctions and equilibrium problems
Bianchi, M
Schaible, S
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1996, 90 (01) : 31 - 43
[6] Equilibrium Problems with Generalized Monotone Bifunctions and Applications to Variational Inequalities
O. Chaldi
Z. Chbani
H. Riahi
[J]. Journal of Optimization Theory and Applications, 2000, 105 (2) : 299 - 323
[7] Facchinei F., 2007, Finite-Dimensional Variational Inequalities and Complementarity Problems
[8] Fan Ky., 1972, Inequalities, P103
[9] Giannessi F., 2004, Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models
[10] Fixed point optimization algorithm and its application to power control in CDMA data networks
Iiduka, Hideaki
[J]. MATHEMATICAL PROGRAMMING, 2012, 133 (1-2) : 227 - 242

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