Forward-Backward algorithms for weakly convex problems
Optimization and Control
2024-06-24 v3
Abstract
We investigate the convergence properties of exact and inexact forward-backward algorithms to minimise the sum of two weakly convex functions defined on a Hilbert space, where one has a Lipschitz-continuous gradient. We show that the exact forward-backward algorithm converges strongly to a global solution, provided that the objective function satisfies a sharpness condition. For the inexact forward-backward algorithm, the same condition ensures that the distance from the iterates to the solution set approaches a positive threshold depending on the accuracy level of the proximal computations. As an application of the considered setting, we provide numerical experiments related to discrete tomography.
Cite
@article{arxiv.2303.14021,
title = {Forward-Backward algorithms for weakly convex problems},
author = {Ewa Bednarczuk and Giovanni Bruccola and Gabriele Scrivanti and The Hung Tran},
journal= {arXiv preprint arXiv:2303.14021},
year = {2024}
}