Inertial Bregman Proximal Gradient Algorithm For Nonconvex Problem with Smooth Adaptable Property

TL;DR

This paper introduces an inertial Bregman Proximal Gradient algorithm tailored for nonconvex optimization problems with a smooth adaptable property, providing convergence guarantees under certain conditions.

Contribution

It develops a novel inertial Bregman Proximal Gradient method for nonconvex problems with weaker smoothness assumptions and establishes its convergence properties.

Findings

Proves stationary convergence of the inertial BPG algorithm.

Establishes sublinear convergence rate.

Guarantees global convergence under KL property.

Abstract

In this paper we study the problems of minimizing the sum of two nonconvex functions: one is differentiable and satisfies smooth adaptable property. The smooth adaptable property, also named relatively smooth condition, is weaker than the globally gradient Lipschitz continuity. We analyze an inertial version of the Bregman Proximal Gradient (BPG) algorithm and prove its stationary convergence. Besides, we prove a sublinear convergence of the inertial algorithm. Moreover, if the objective function satisfies Kurdyka--{\L}ojasiewicz (KL) property, its global convergence to a critical point of the objective function can be also guaranteed.