Inertial extragradient-viscosity algorithms for nonmonotone and non-Lipschitzian equilibrium problems in Hilbert spaces

Abstract

In this paper, combining line-search technique with viscosity method, inertial algorithm and subgradient algorithm, we propose a new iterative algorithm that does not involve in projection operators to solve the nonmonotone and non-Lipschitzian equilibrium problem in Hilbert space and obtain the strong convergence theorem. In addition, we also use our main result to the variational inequality and the convex minimization problem, and obtain the corresponding strong convergence theorems.