Iterative Method with Inertia for Variational Inequalities on Hadamard Manifolds with Lower Bounded Curvature

Abstract

In this paper, we are concerned with solving variational inequalities on Hadamard manifolds, the curvature of which is bounded from below. The underlying vector field is assumed to be continuous and pseudomonotone. By combining the hyperplane projection method and the inertial extrapolation technique, a Halpern-type method is proposed. Under some mild assumptions, global convergence of the proposed algorithm is established. Numerical experiments are reported to show the efficiency of the proposed algorithm.