# A new envelope function for nonsmooth DC optimization

arXiv: https://arxiv.org/abs/2004.00083 · HTML: https://mlsanity.com/paper/2004.00083/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Mar 2020.

## Built on by (most cited first, 1 of 1)

- [Lasry-Lions Envelopes and Nonconvex Optimization: A Homotopy Approach](https://mlsanity.com/paper/2103.08533/) (2021)

## Abstract (arXiv)

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.