Convergence rate of a relaxed inertial proximal algorithm for convex minimization. (2nd June 2020)

• Record Type: Journal Article
• Authors: Attouch, Hedy; Cabot, Alexandre
• Is Part Of: Optimization. Volume 69:Number 6(2020)
• Page Start: 1281
• Page End: 1312
• Publication Date: 2020-06-02
• Subjects: Inertial proximal method -- Lyapunov analysis -- maximally monotone operators -- nonsmooth convex minimization -- relaxation; 49M37 -- 65K05 -- 65K10 -- 90C25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1696337
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In a Hilbert space setting, the authors recently introduced a general class of relaxed inertial proximal algorithms that aim to solve monotone inclusions. In this paper, we specialize this study in the case of non-smooth convex minimization problems. We obtain convergence rates for values which have similarities with the results based on the Nesterov accelerated gradient method. The joint adjustment of inertia, relaxation and proximal terms plays a central role. In doing so, we highlight inertial proximal algorithms that converge for general monotone inclusions, and which, in the case of convex minimization, give fast convergence rates of values in the worst case.