Lasry-Lions Envelopes and Nonconvex Optimization: A Homotopy Approach

Miguel Simões, Andreas Themelis, Panagiotis Patrinos

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

Abstract

In large-scale optimization, the presence of nonsmooth and nonconvex terms in a given problem typically makes it hard to solve. A popular approach to address nonsmooth terms in convex optimization is to approximate them with their respective Moreau envelopes. In this work, we study the use of Lasry-Lions double envelopes to approximate nonsmooth terms that are also not convex. These envelopes are an extension of the Moreau ones but exhibit an additional smoothness property that makes them amenable to fast optimization algorithms. Lasry-Lions envelopes can also be seen as an “intermediate” between a given function and its convex envelope, and we make use of this property to develop a method that builds a sequence of approximate subproblems that are easier to solve than the original problem. We discuss convergence properties of this method when used to address composite minimization problems; additionally, based on a number of experiments, we discuss settings where it may be more useful than classical alternatives in two domains: signal decoding and spectral unmixing.

Original languageEnglish
Title of host publication29th European Signal Processing Conference, EUSIPCO 2021 - Proceedings
PublisherEuropean Signal Processing Conference, EUSIPCO
Pages2089-2093
Number of pages5
ISBN (Electronic)9789082797060
DOIs
Publication statusPublished - 2021
Event29th European Signal Processing Conference, EUSIPCO 2021 - Dublin, Ireland
Duration: Aug 23 2021Aug 27 2021

Publication series

NameEuropean Signal Processing Conference
Volume2021-August
ISSN (Print)2219-5491

Conference

Conference29th European Signal Processing Conference, EUSIPCO 2021
Country/TerritoryIreland
CityDublin
Period8/23/218/27/21

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering

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