Korpelevich's method for variational inequality problems on Hadamard manifolds

Authors:
Guo-Ji Tang;Nan-Jing Huang
Affiliations:
Department of Mathematics, Sichuan University, Chengdu, People's Republic of China 610064;Department of Mathematics, Sichuan University, Chengdu, People's Republic of China 610064
Venue:
Journal of Global Optimization
Year:
2012

Citing 5
Cited 0

Subgradient algorithm on Riemannian manifolds

Journal of Optimization Theory and Applications
A New Projection Method for Variational Inequality Problems

SIAM Journal on Control and Optimization
Variational inequalities on Hadamard manifolds

Nonlinear Analysis: Theory, Methods & Applications
Singularities of Monotone Vector Fields and an Extragradient-type Algorithm

Journal of Global Optimization
Korpelevich's method for variational inequality problems in Banach spaces

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

The concept of pseudomonotone vector field on Hadamard manifold is introduced. A variant of Korpelevich's method for solving the variational inequality problem is extended from Euclidean spaces to constant curvature Hadamard manifolds. Under a pseudomonotone assumption on the underlying vector field, we prove that the sequence generated by the method converges to a solution of variational inequality, whenever it exists. Moreover, we give an example to show the effectiveness of our method.