New Convergence Theorems for Pseudomonotone Variational Inequality on Hadamard Manifolds

Abstract

In this paper, we propose an efficient viscosity type subgradient extragradient algorithm for solving pseudomonotone variational inequality on Hadamard manifolds which is of symmetrical characteristic. Under suitable conditions, we obtain the convergence of the iteration sequence generated by the proposed algorithm to a solution of a pseudomonotone variational inequality on Hadamard manifolds. We also employ our main result to solve a constrained convex minimization problem and present a numerical experiment to illustrate the asymptotic behavior of the algorithm. Our results develop and improve some recent results.

Keywords

• pseudomonotone mapping
• variational inequality
• Hadamard manifold
• subgradient extragradient method
• viscosity method