Convergence analysis of a stochastic heavy-ball method for linear ill-posed problems

TL;DR

This paper analyzes a stochastic heavy-ball method for linear ill-posed inverse problems, establishing its regularization properties and convergence rates with numerical validation.

Contribution

It introduces a stochastic heavy-ball algorithm tailored for ill-posed problems, demonstrating its regularization ability and convergence behavior under specific conditions.

Findings

The method achieves regularization with proper parameter choices.

Convergence rates are derived under source conditions.

Numerical experiments confirm the theoretical results.

Abstract

In this paper we consider a stochastic heavy-ball method for solving linear ill-posed inverse problems. With suitable choices of the step-sizes and the momentum coefficients, we establish the regularization property of the method under {\it a priori} selection of the stopping index and derive the rate of convergence under a benchmark source condition on the sought solution. Numerical results are provided to test the performance of the method.