Linear convergence of proximal incremental aggregated gradient method for nonconvex nonsmooth minimization problems

Abstract

In this paper, we study the proximal incremental aggregated gradient (PIAG) method for minimizing the sum of smooth component functions and a nonsmooth function, both of which are allowed to be nonconvex. We show the linear convergence rate result under the metric subregularity and proper separation condition. Our method is developed based on a special auxiliary Lyapunov function sequence, and we also show that this auxiliary sequence is Q-linearly convergent. Using this result, we obtain an explicit computable stepsize threshold to guarantee that the objective value and iterative sequences are R-linearly convergent. Preliminary computational experience is also reported.

Keywords:

• Linear convergence
• metrical subregularity
• nonconvex nonsmooth minimization
• proximal incremental aggregated gradient

2010 Mathematics Subject Classifications:

• 90C26
• 90C06
• 90C15

Disclosure statement

No potential conflict of interest was reported by the authors.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.