Inexact proximal ε-subgradient methods for composite convex optimization problems

2018/05/25 by R. Díaz Millán, Millán, Reinier Díaz, Majela Pentón Machado +1
Computer Science · Engineering · #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.1805.10120

openalex publication_date 2018/05/25 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28

Abstract

We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at each iteration, inexact evaluations of the proximal operator and approximate subgradients of the functions (namely: the ε-subgradients). The methods use different error criteria for approximating the proximal operators. We provide an analysis of the convergence and rate of convergence properties of these methods, considering various stepsize rules, including both, diminishing and constant stepsizes. For the case where one of the functions is smooth, we propose an inexact accelerated version of the proximal gradient method, and prove that the optimal convergence rate for the function values can be achieved.

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