INERTIAL TSENG METHOD WITH NONDECREASING ADAPTIVE STEPSIZE FOR VARIATIONAL INEQUALITY ON HADAMARD MANIFOLDS

In this article, we propose an inertial and a viscosity iterative method for solving variational inequality problem on Hadamard manifolds. The iterative algorithm is inspired by Tseng’s extragradient method with a self-adaptive procedure which generates dynamic step-sizes converging to a positive constant. The proposed method does not require the knowledge of the Lipschitz constant as well as the sequential weak continuity of the corresponding operator. Under a pseudomono-tone assumption on the underlying vector field, we establish a convergence result for solving a pseudomonotone variational inequality and fixed point problems of nonexpansive mapping under some mild assump-tions. Finally, we present some fundamental experiment to illustrate the numerical behavior of our proposed method. The result discussed in this article extends and complements many related results in the literature.