A stochastic two-step inertial Bregman proximal alternating linearized minimization algorithm for nonconvex and nonsmooth problems

TL;DR

This paper introduces a stochastic inertial Bregman proximal alternating linearized minimization algorithm with variance reduction for large-scale nonconvex, nonsmooth optimization, demonstrating convergence and practical effectiveness.

Contribution

It proposes a novel stochastic two-step inertial Bregman proximal algorithm with variance reduction, extending convergence analysis to nonconvex, nonsmooth problems.

Findings

Convergence to critical points under certain conditions.

Effective in sparse nonnegative matrix factorization.

Successful application to blind image deblurring.

Abstract

In this paper, for solving a broad class of large-scale nonconvex and nonsmooth optimization problems, we propose a stochastic two step inertial Bregman proximal alternating linearized minimization (STiBPALM) algorithm with variance-reduced stochastic gradient estimators. And we show that SAGA and SARAH are variance-reduced gradient estimators. Under expectation conditions with the Kurdyka-Lojasiewicz property and some suitable conditions on the parameters, we obtain that the sequence generated by the proposed algorithm converges to a critical point. And the general convergence rate is also provided. Numerical experiments on sparse nonnegative matrix factorization and blind image-deblurring are presented to demonstrate the performance of the proposed algorithm.