A self-adaptive viscosity-type inertial extragradient algorithm for solving monotone variational inequality and paramonotone equilibrium problem 1

Abstract

In this paper, we introduce a self-adaptive viscosity-type inertial extragradient algorithm to solve monotone variational inequality problem and paramonotone equilibrium problem in real Hilbert space. Based on the self-adaptive method, inertial technique is used to accelerate the convergence rate of the method. Under the assumption of monotonicity of the related mappings, the strong convergence of the iterative algorithm is established. The results presented here improve and generalize many existing results in this direction. Mathmatical subject classification: Primary: 90C33; Secondary: 49J52