AN EXTRAGRADIENT METHOD FOR VECTOR EQUILIBRIUM PROBLEMS ON HADAMARD MANIFOLDS

被引：11

作者：

Iusem, Alfredo N. ^{[1
]}

Mohebbi, Vahid ^{[2
]}

机构：

[1] Inst Matematica Pura & Aplicada, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, RJ, Brazil

[2] Univ Texas El Paso, Dept Pharmaceut Sci, 500 W Univ Ave, El Paso, TX 79968 USA

来源：

JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS | 2021年 / 5卷 / 03期

关键词：

Extragradient method; Hadamard manifold; Linesearch; Vector equilibrium problem; Vector valued bifunction; GENERALIZED MONOTONE BIFUNCTIONS; PROXIMAL POINT ALGORITHM; VARIATIONAL-INEQUALITIES; OPTIMIZATION; EXISTENCE;

D O I：

10.23952/jnva.5.2021.3.09

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the vector equilibrium problem in Hadamard manifolds, which extends the scalar equilibrium problem to vector valued bifunctions. We propose an extragradient method for solving this problem. Under suitable assumptions on the bifunction, we prove that the generated sequence converges to a solution of the problem. We also give some examples of Hadamard manifolds and vector equilibrium problems to which our main result can be applied. Finally, we present some numerical experiments.

引用

页码：459 / 476

页数：18

共 50 条

[21] Extragradient method with Bregman distances for solving vector quasi-equilibrium problems
Vahid Mohebbi
Computational and Applied Mathematics, 2022, 41
[22] Vector variational inequalities and vector optimization problems on Hadamard manifolds
Chen, Sheng-lan
Huang, Nan-jing
OPTIMIZATION LETTERS, 2016, 10 (04) : 753 - 767
[23] EXTRAGRADIENT METHODS FOR QUASI-EQUILIBRIUM PROBLEMS IN BANACH SPACES
Rouhani, Behzad Djafari
Mohebbi, Vahid
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2022, 112 (01) : 90 - 114
[24] A new regularization of equilibrium problems on Hadamard manifolds: applications to theories of desires
Bento, G. C.
Cruz Neto, J. X.
Soares Jr, P. A.
Soubeyran, A.
ANNALS OF OPERATIONS RESEARCH, 2022, 316 (02) : 1301 - 1318
[25] Abstract generalized vector quasi-equilibrium problems in noncompact Hadamard manifolds
Lu, Haishu
Wang, Zhihua
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017,
[26] An Existence Result for the Generalized Vector Equilibrium Problem on Hadamard Manifolds
Batista, E. E. A.
Bento, G. C.
Ferreira, O. P.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2015, 167 (02) : 550 - 557
[27] Some algorithms for equilibrium problems on Hadamard manifolds
Muhammad Aslam Noor
Khalida Inayat Noor
Journal of Inequalities and Applications, 2012
[28] Some algorithms for equilibrium problems on Hadamard manifolds
Noor, Muhammad Aslam
Noor, Khalida Inayat
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2012,
[29] Necessary and Sufficient Optimality Conditions for Vector Equilibrium Problems on Hadamard Manifolds
Ruiz-Garzon, Gabriel
Osuna-Gomez, Rafaela
Ruiz-Zapatero, Jaime
SYMMETRY-BASEL, 2019, 11 (08):
[30] Mixed vector equilibrium-like problems on Hadamard manifolds: error bound analysis
Hung, Nguyen Van
Tam, Vo Minh
O'Regan, Donal
APPLICABLE ANALYSIS, 2023, 102 (05) : 1530 - 1546

← 1 2 3 4 5 →