An Extragradient-type Algorithm for Variational Inequality on Hadamard Manifolds

E. E. A. Batista, G. C. Bento, O. P. Ferreira

Published 2018-04-24Version 1

The aim of this paper is to present an extragradient method for variational inequality associated to a point-to-set vector field in Hadamard manifolds and to study its convergence properties. In order to present our method the concept of $\epsilon$-enlargement of maximal monotone vector fields is used and its lower-semicontinuity is stablished in order to obtain the convergence of the method in this new context.