Solving common nonmonotone equilibrium problems using an inertial parallel hybrid algorithm with Armijo line search with applications to image recovery

Abstract

Abstract In this work, we modify the inertial hybrid algorithm with Armijo line search using a parallel method to approximate a common solution of nonmonotone equilibrium problems in Hilbert spaces. A weak convergence theorem is proved under some continuity and convexity assumptions on the bifunction and the nonemptiness of the common solution set of Minty equilibrium problems. Furthermore, we demonstrate the quality of our inertial parallel hybrid algorithm by using image restoration, as well as its superior efficiency when compared with previously considered parallel algorithms.

Keywords

• Armijo line search
• Nonmonotone equilibrium problems
• Bifunctions
• Hilbert space
• Inertial technique