A new envelope function for nonsmooth DC optimization
Optimization and Control
2024-04-17 v1
Abstract
Difference-of-convex (DC) optimization problems are shown to be equivalent to the minimization of a Lipschitz-differentiable "envelope". A gradient method on this surrogate function yields a novel (sub)gradient-free proximal algorithm which is inherently parallelizable and can handle fully nonsmooth formulations. Newton-type methods such as L-BFGS are directly applicable with a classical linesearch. Our analysis reveals a deep kinship between the novel DC envelope and the forward-backward envelope, the former being a smooth and convexity-preserving nonlinear reparametrization of the latter.
Cite
@article{arxiv.2004.00083,
title = {A new envelope function for nonsmooth DC optimization},
author = {Andreas Themelis and Ben Hermans and Panagiotis Patrinos},
journal= {arXiv preprint arXiv:2004.00083},
year = {2024}
}