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:Proceedings of the IEEE Conference on Decision & Control pp. 4697 - 4702
Main Authors: Themelis, Andreas, Hermans, Ben, Patrinos, Panagiotis
Format: Conference Proceeding
Language:English
Published: IEEE 14.12.2020
Subjects:
Convex functions
Gradient methods
Minimization
Optimization
Radio frequency
Splines (mathematics)
Symmetric matrices
ISSN:2576-2370
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.
ISSN:2576-2370
DOI:10.1109/CDC42340.2020.9304514