Two accelerated double inertial algorithms for variational inequalities on Hadamard manifolds

Abstract

Two modified double inertial proximal point algorithms are proposed for solving variational inequality problems with a pseudomonotone vector field in the settings of a Hadamard manifold. Weak convergence of the proposed methods is attained without the requirement of Lipschitz continuity conditions. The convergence efficiency of the proposed algorithms is improved with the help of the double inertial technique and the non-monotonic self-adaptive step size rule. We present a numerical experiment to demonstrate the effectiveness of the proposed algorithm compared to several existing ones. The results extend and generalize many recent methods in the literature.