Convergence Results of Two-Step Inertial Proximal Point Algorithm

2022/07/20 by Olaniyi S. Iyiola, Iyiola, Olaniyi S., Yekini Shehu +1
Computer Science · Mathematics · #49M25 #68Q25 #90C22 #90C25 #90C30 #90C60 #Advanced Optimization Algorithms Research #FOS: Mathematics #Fixed Point Theorems Analysis #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2207.09668

openalex publication_date 2022/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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