Convergence results of two-step inertial proximal point algorithm

• DOI: 10.1016/j.apnum.2022.07.013
• Publication Date: 2022-08-01T11:19:00Z
• Authors: Olaniyi S. Iyiola; Yekini Shehu
• Keywords: Optimization and Control (math.OC); FOS: Mathematics; 0211 other engineering and technologies; 02 engineering and technology; Mathematics - Optimization and Control; 90C25, 90C30, 90C60, 68Q25, 49M25, 90C22

26 pages<br/>This paper proposes a two-point inertial proximal point algorithm to find zero of maximal monotone operators in Hilbert spaces. We obtain weak convergence results and non-asymptotic $O(1/n)$ convergence rate of our proposed algorithm in non-ergodic sense. Applications of our results to various well-known convex optimization methods, such as the proximal method of multipliers and the alternating direction method of multipliers are given. Numerical results are given to demonstrate the accelerating behaviors of our method over other related methods in the literature.<br/>