An Algorithm for Solving Common Points of Convex Minimization Problems with Applications

Abstract

In algorithm development, symmetry plays a vital part in managing optimization problems in scientific models. The aim of this work is to propose a new accelerated method for finding a common point of convex minimization problems and then use the fixed point of the forward-backward operator to explain and analyze a weak convergence result of the proposed algorithm in real Hilbert spaces under certain conditions. As applications, we demonstrate the suggested method for solving image inpainting and image restoration problems.

Keywords

• Hilbert space
• forward-backward algorithm
• convergence theorems
• convex minimization problems
• fixed point