A new envelope function for nonsmooth DC optimization

Andreas Themelis, Ben Hermans, Panagiotis Patrinos

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

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.

Original languageEnglish
Title of host publication2020 59th IEEE Conference on Decision and Control, CDC 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4697-4702
Number of pages6
ISBN (Electronic)9781728174471
DOIs
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
Volume2020-December
ISSN (Print)0743-1546

Conference

Conference59th IEEE Conference on Decision and Control, CDC 2020
CountryKorea, Republic of
CityVirtual, Jeju Island
Period12/14/2012/18/20

All Science Journal Classification (ASJC) codes

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

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