Solving Common Nonmonotone Equilibrium Problems Using a Parallel Inertial Type Algorithm with Armijo Linesearch

Kunrada Kankam, Wanida Wongjak, Jirapa Kotcharerg, Watcharaporn Cholamjiak

Abstract

In this work, we study an iterative method with an inertial term extrapolation step and parallel algorithm for solving common equilibrium problems of nonmonotone bifunctions in real Hilbert spaces. The inertial term extrapolation step is introduced to speed up the rate of convergence of the iteration process. We obtain weak convergence results under some continuity and convexity assumptions on the bifunction and the condition that the common solution set of the associated Minty equilibrium problems is nonempty. We also give some numerical experiments of our algorithm which are defined by parallel inertial type algorithm to show the efficiency and implementation for LASSO problem in signal recovery in situation different types of blurred matrices.