Inertial Proximal Incremental Aggregated Gradient Method

TL;DR

This paper introduces an inertial variant of the Proximal Incremental Aggregated Gradient method (iPIAG) that achieves global linear convergence under weaker conditions than strong convexity, with demonstrated numerical improvements.

Contribution

The paper proposes the inertial iPIAG method, extending PIAG with inertial terms, and proves its convergence under quadratic growth conditions, along with empirical validation.

Findings

iPIAG converges linearly under quadratic growth conditions.

Numerical experiments show iPIAG outperforms PIAG.

The method is effective for convex optimization with nonsmooth regularization.

Abstract

In this paper, we introduce an inertial version of the Proximal Incremental Aggregated Gradient method (PIAG) for minimizing the sum of smooth convex component functions and a possibly nonsmooth convex regularization function. Theoretically, we show that the inertial Proximal Incremental Aggregated Gradiend (iPIAG) method enjoys a global linear convergence under a quadratic growth condition, which is strictly weaker than strong convexity, provided that the stepsize is not larger than a constant. Moreover, we present two numerical expreiments which demonstrate that iPIAG outperforms the original PIAG.