On inexact relative-error hybrid proximal extragradient,\n forward-backward and Tseng's modified forward-backward methods with inertial\n effects

2018/12/05 by M. Marques Alves, R. T. Marcavillaca, Alves, M. Marques +1 · 1 citation
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1812.02138

openalex publication_date 2018/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we propose and study the asymptotic convergence and\nnonasymptotic global convergence rates (iteration-complexity) of an inertial\nunder-relaxed version of the relative-error hybrid proximal extragradient (HPE)\nmethod for solving monotone inclusion problems. We analyze the proposed method\nunder more flexible assumptions than existing ones on the extrapolation and\nrelative-error parameters. As applications, we propose and/or study inertial\nunder-relaxed forward-backward and Tseng's modified forward-backward type\nmethods for solving structured monotone inclusions.\n

Citations

• Splitting Algorithms for the Sum of Two Nonlinear Operators
• Monotone Operators and the Proximal Point Algorithm
• Fast convex optimization via inertial dynamics with Hessian driven\n damping

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