Regularized HPE-type methods for solving monotone inclusions with\n improved pointwise iteration-complexity bounds

2015/09/08 by M. Marques Alves, Renato D. C. Monteiro, Alves, Maicon Marques +3
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1509.02255

openalex publication_date 2015/09/08 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

This paper studies the iteration-complexity of new regularized hybrid\nproximal extragradient (HPE)-type methods for solving monotone inclusion\nproblems (MIPs). The new (regularized HPE-type) methods essentially consist of\ninstances of the standard HPE method applied to regularizations of the original\nMIP. It is shown that its pointwise iteration-complexity considerably improves\nthe one of the HPE method while approaches (up to a logarithmic factor) the\nergodic iteration-complexity of the latter method.\n

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