A new envelope function for nonsmooth DC optimization

Andreas Themelis, Ben Hermans, Panagiotis Patrinos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)


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.

Original languageEnglish
Title of host publication2020 59th IEEE Conference on Decision and Control, CDC 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781728174471
Publication statusPublished - Dec 14 2020
Externally publishedYes
Event59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of
Duration: Dec 14 2020Dec 18 2020

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546


Conference59th IEEE Conference on Decision and Control, CDC 2020
Country/TerritoryKorea, Republic of
CityVirtual, Jeju Island

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization


Dive into the research topics of 'A new envelope function for nonsmooth DC optimization'. Together they form a unique fingerprint.

Cite this