Moreau Envelope ADMM for Decentralized Weakly Convex Optimization

Reza Mirzaeifard, Naveen K.D. Venkategowda, Alexander Jung*, Stefan Werner

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

Abstract

This paper proposes a proximal variant of the alternating direction method of multipliers (ADMM) for distributed optimization. Although the current versions of ADMM algorithm provide promising numerical results in producing solutions that are close to optimal for many convex and non-convex optimization problems, it remains unclear if they can converge to a stationary point for weakly convex and locally non-smooth functions. Through our analysis using the Moreau envelope function, we demonstrate that MADM can indeed converge to a stationary point under mild conditions. Our analysis also includes computing the bounds on the amount of change in the dual variable update step by relating the gradient of the Moreau envelope function to the proximal function. Furthermore, the results of our numerical experiments indicate that our method is faster and more robust than widely-used approaches.

Original languageEnglish
Title of host publication2023 Asia Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA ASC 2023
PublisherIEEE
Pages1126-1130
Number of pages5
ISBN (Electronic)979-8-3503-0067-3
DOIs
Publication statusPublished - 2023
MoE publication typeA4 Conference publication
EventAsia-Pacific Signal and Information Processing Association Annual Summit and Conference - Taipei, Taiwan, Republic of China
Duration: 31 Oct 20233 Nov 2023

Publication series

NameProceedings / Asia-Pacific Signal and Information Processing Association Annual Summit and Conference APSIPA ASC
ISSN (Electronic)2640-0103

Conference

ConferenceAsia-Pacific Signal and Information Processing Association Annual Summit and Conference
Abbreviated titleAPSIPA ASC
Country/TerritoryTaiwan, Republic of China
CityTaipei
Period31/10/202303/11/2023

Keywords

  • ADMM
  • Distributed optimization
  • Moreau envelope
  • non-convex and nonsmooth optimization
  • weakly convex functions

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