2019/08/29 by Fuying Cui, Yang Yang, Cui, Fuying +4
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1908.11029
openalex publication_date 2019/08/29 · openalex created_date 2019/09/05 · openalex updated_date 2026/07/28
The classical Krasnoselskii-Mann iteration is broadly used for approximating fixed points of nonexpansive operators. To accelerate the convergence of the Krasnoselskii-Mann iteration, the inertial methods were received much attention in recent years. In this paper, we propose an inexact inertial Krasnoselskii-Mann algorithm. In comparison with the original inertial Krasnoselskii-Mann algorithm, our algorithm allows error for updating the iterative sequence, which makes it more flexible and useful in practice. We establish weak convergence results for the proposed algorithm under different conditions on parameters and error terms. Furthermore, we provide a nonasymptotic convergence rate for the proposed algorithm. As applications, we propose and study inexact inertial proximal point algorithm and inexact inertial forward-backward splitting algorithm for solving monotone inclusion problems and the corresponding convex minimization problems.