A new envelope function for nonsmooth DC optimization

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...

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Bibliographic Details
Published in:arXiv.org
Main Authors: Themelis, Andreas, Hermans, Ben, Patrinos, Panagiotis
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 31.03.2020
Subjects:
Algorithms
Convexity
Optimization
Parallel processing
ISSN:2331-8422
Online Access:Get full text
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Summary: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.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.2004.00083