1Department of Mathematics, Aligarh Muslim University, Aligarh
2Department of Applied Mathematics, Aligarh Muslim University, Aligarh
*E-mail: *qhansari@gmail.com
In this article, we study variational inequalities and optimization problems in the setting of Hadamard manifolds. We discuss the relationship among these problems under different conditions. We compose an Armijo’s type extragradient algorithm to compute an approximate solution of the variational inequality problem (in short, VIP) which does not require the monotonicity of the objective vector field and nonemptiness of the solution set of VIP. We discuss the convergence result of the proposed algorithm under mild assumptions. Several appropriate examples are also presented at suitable places.
AMS Subject Classification: [2010] 49J53; 49J52; 90C29; 90C30
Variational inequalities, Extragradient-type algorithm, Geodesic, Quasiconvexity, Hemicontinuity, Riemannian metric, Hadamard manifolds
