On the convergence of a linesearch based proximal-gradient method for nonconvex optimization

TL;DR

This paper introduces a variable metric linesearch proximal gradient method for nonconvex optimization, proving its convergence under certain conditions and demonstrating its effectiveness in image processing tasks.

Contribution

It presents a novel convergence proof for a linesearch-based proximal gradient method applied to nonconvex problems, with practical validation in image processing applications.

Findings

Converges to critical points under Kurdyka-Lojasiewicz property.

Flexible and robust in various image processing tasks.

Competitive performance compared to recent methods.

Abstract

We consider a variable metric linesearch based proximal gradient method for the minimization of the sum of a smooth, possibly nonconvex function plus a convex, possibly nonsmooth term. We prove convergence of this iterative algorithm to a critical point if the objective function satisfies the Kurdyka-Lojasiewicz property at each point of its domain, under the assumption that a limit point exists. The proposed method is applied to a wide collection of image processing problems and our numerical tests show that our algorithm results to be flexible, robust and competitive when compared to recently proposed approaches able to address the optimization problems arising in the considered applications.