ITERATIVE ALGORITHMS FOR PSEUDOMONOTONE VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS ON HADAMARD MANIFOLDS

被引：0

作者：

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

Uddin, Moin ^{[1
]}

YAOt, Jen-chih ^{[1
]}

机构：

[1] Aligarh Muslim Univ, Dept Math, Aligarh, India

[2] Chongqing Univ Technol, Coll Sci, Chongqing 400054, Peoples R China

来源：

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2023年 / 24卷 / 05期

关键词：

Variational inequality problems; fixed point problems; pseudomonotone vector fields; nonexpansive mappings; Hadamard manifolds; MONOTONE VECTOR-FIELDS; INCLUSION PROBLEMS; PROJECTION;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The present paper proposes two iterative algorithms, namely, Mann type and Halpern type, for finding a common solution of the pseudomonotone variational inequality problems and a fixed point problem of nonexpansive mappings in the setting of Hadamard manifolds. The convergence analysis of the proposed algorithms is studied without prior knowledge of the Lipschitz constant of the involved vector field. A computational experiment to illustrate the efficiency of the proposed algorithms is given.

引用

页码：1043 / 1063

页数：21

共 27 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] Regularization methods for hierarchical variational inequality problems on Hadamard manifolds [J].

Ansari, Qamrul Hasan ;

Babu, Feeroz ;

Uddin, Moin .

ARABIAN JOURNAL OF MATHEMATICS, 2023, 12 (02) :309-330

[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] Regularization of proximal point algorithms in Hadamard manifolds [J].

Ansari, Qamrul Hasan ;

Babu, Feeroz ;

Yao, Jen-Chih .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2019, 21 (01)

[5]

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

[6] Proximal point method for a special class of nonconvex functions on Hadamard manifolds [J].

Bento, G. C. ;

Ferreira, O. P. ;

Oliveira, P. R. .

OPTIMIZATION, 2015, 64 (02) :289-319

[7] Modified Tseng's extragradient methods for variational inequality on Hadamard manifolds [J].

Chen, Junfeng ;

Liu, Sanyang ;

Chang, Xiaokai .

APPLICABLE ANALYSIS, 2021, 100 (12) :2627-2640

[8] 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

[9]

do Carmo M, 1976, Differential Geometry of Curves and Surfaces

[10] Proximal point algorithm on Riemannian manifolds [J].

Ferreira, OP ;

Oliveira, PR .

OPTIMIZATION, 2002, 51 (02) :257-270

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