Korpelevich’s method for variational inequality problems on Hadamard manifolds

2011 ◽  
Vol 54 (3) ◽  
pp. 493-509 ◽  
Author(s):  
Guo-ji Tang ◽  
Nan-jing Huang
Keyword(s):  
Variational Inequality ◽  
Variational Inequality Problems ◽  
Hadamard Manifolds

scholarly journals Iterative algorithm for singularities of inclusion problems in Hadamard manifolds

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Parin Chaipunya ◽  
Konrawut Khammahawong ◽  
Poom Kumam
Keyword(s):  
Variational Inequality ◽  
Iterative Algorithm ◽  
Convex Minimization ◽  
Variational Inequality Problems ◽  
Hadamard Manifolds ◽  
Inclusion Problems ◽  
Numerical Example ◽  
Minimization Problems ◽  
Convex Minimization Problems

AbstractThe main purpose of this paper is to introduce a new iterative algorithm to solve inclusion problems in Hadamard manifolds. Moreover, applications to convex minimization problems and variational inequality problems are studied. A numerical example also is presented to support our main theorem.

scholarly journals New Tseng’s extragradient methods for pseudomonotone variational inequality problems in Hadamard manifolds

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Konrawut Khammahawong ◽  
Poom Kumam ◽  
Parin Chaipunya ◽  
Somyot Plubtieng
Keyword(s):  
Variational Inequality ◽  
Numerical Experiments ◽  
Vector Fields ◽  
Variational Inequality Problem ◽  
Variational Inequality Problems ◽  
Hadamard Manifolds ◽  
Extragradient Methods ◽  
Continuous Vector ◽  
Inequality Problem ◽  
Lipschitz Continuous

AbstractWe propose Tseng’s extragradient methods for finding a solution of variational inequality problems associated with pseudomonotone vector fields in Hadamard manifolds. Under standard assumptions such as pseudomonotone and Lipschitz continuous vector fields, we prove that any sequence generated by the proposed methods converges to a solution of variational inequality problem, whenever it exits. Moreover, we give some numerical experiments to illustrate our main results.

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