VISCOSITY METHOD WITH A φ-CONTRACTION MAPPING FOR HIERARCHICAL VARIATIONAL INEQUALITIES ON HADAMARD MANIFOLDS

被引：14

作者：

Al-Homidan, Suliman ^{[1
]}

Ansari, Qamrul Hasan ^{[1
,2
]}

Babu, Feeroz ^{[2
,3
]}

Yao, Jen-Chih ^{[4
]}

机构：

[1] King Fahd Univ Petr & Minerals, Dept Math & Stat, Dhahran, Saudi Arabia

[2] Aligarh Muslim Univ, Dept Math, Aligarh, Uttar Pradesh, India

[3] Natl Sun Yat Sen Univ, Kaohsiung, Taiwan

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

来源：

FIXED POINT THEORY | 2020年 / 21卷 / 02期

关键词：

Viscosity method; phi-contraction mappings; hierarchical variational inequality problem; Moreau-Yosida regularization; hierarchical minimization problem; Hadamard manifolds; monotone vector fields; geodesic convexity; nonexpansive mappings; PROXIMAL POINT ALGORITHM; APPROXIMATION METHODS; INCLUSION PROBLEMS; FIXED-POINTS;

D O I：

10.24193/fpt-ro.2020.2.40

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose the viscosity method for solving variational inequality problems defined over a set of fixed points of a nonexpansive mapping and involving a phi-contraction mapping and another nonexpansive mapping in the setting of Hadamard manifolds. Several special cases of such a variational inequality problem are also considered. The convergence analysis of the proposed method is studied. We illustrate proposed algorithm and convergence result by a numerical example. The algorithms and convergence results of this paper extend and improve several known algorithms and results from linear structure to Hadamard manifolds.

引用

页码：561 / 584

页数：24

共 30 条

[1] Halpern- and Mann-Type Algorithms for Fixed Points and Inclusion Problems on Hadamard Manifolds [J].

Al-Homidan, Suliman ;

Ansari, Qamrul Hasan ;

Babu, Feeroz .

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2019, 40 (06) :621-653

[2]

Alber Ya. I., 1997, New Results in Operator Theory and Its Applications, Operator Theory: Advances and Applications, V98, P7

[3] Proximal point algorithm for inclusion problems in Hadamard manifolds with applications [J].

Ansari, Qamrul Hasan ;

Babu, Feeroz .

OPTIMIZATION LETTERS, 2021, 15 (03) :901-921

[4]

Ansari QH, 2018, J NONLINEAR CONVEX A, V19, P219

[5] COMPUTING MEDIANS AND MEANS IN HADAMARD SPACES [J].

Bacak, Miroslav .

SIAM JOURNAL ON OPTIMIZATION, 2014, 24 (03) :1542-1566

[6] ON NONLINEAR CONTRACTIONS [J].

BOYD, DW ;

WONG, JSW .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 20 (02) :458-&

[7]

Bridson M., 1999, METRIC SPACES NONPOS

[8] Proximal point algorithm controlled by a slowly vanishing term: Applications to hierarchical minimization [J].

Cabot, A .

SIAM JOURNAL ON OPTIMIZATION, 2005, 15 (02) :555-572

[9]

Cruz J. X., 2000, BALK J GEOM APPL, V5, P69

[10] Convex- and monotone-transformable mathematical programming problems and a proximal-like point method [J].

Da Cruz Neto, J. X. ;

Ferreira, O. P. ;

Perez, L. R. Lucambio ;

Nemeth, S. Z. .

JOURNAL OF GLOBAL OPTIMIZATION, 2006, 35 (01) :53-69

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