Adaptive relaxed ADMM: Convergence theory and practical implementation

Zheng Xu*, Mário T. Figueiredo, Xiaoming YUAN, Christoph Studer, Tom Goldstein

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingConference contributionpeer-review

11 Citations (Scopus)

Abstract

Many modern computer vision and machine learning applications rely on solving difficult optimization problems that involve non-differentiable objective functions and constraints. The alternating direction method of multipliers (ADMM) is a widely used approach to solve such problems. Relaxed ADMM is a generalization of ADMM that often achieves better performance, but its efficiency depends strongly on algorithm parameters that must be chosen by an expert user. We propose an adaptive method that automatically tunes the key algorithm parameters to achieve optimal performance without user oversight. Inspired by recent work on adaptivity, the proposed adaptive relaxed ADMM (ARADMM) is derived by assuming a Barzilai-Borwein style linear gradient. A detailed convergence analysis of ARADMM is provided, and numerical results on several applications demonstrate fast practical convergence.

Original languageEnglish
Title of host publicationProceedings - 30th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages7234-7243
Number of pages10
ISBN (Electronic)9781538604571
DOIs
Publication statusPublished - 6 Nov 2017
Event30th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017 - Honolulu, United States
Duration: 21 Jul 201726 Jul 2017

Publication series

NameProceedings - 30th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017
Volume2017-January

Conference

Conference30th IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017
Country/TerritoryUnited States
CityHonolulu
Period21/07/1726/07/17

Scopus Subject Areas

  • Signal Processing
  • Computer Vision and Pattern Recognition

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