Linearized alternating direction method of multipliers for constrained linear least-squares problem

Raymond H. CHAN*, Min TAO*, Xiaoming YUAN*

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

17 Citations (Scopus)

Abstract

The alternating direction method of multipliers (ADMM) is applied to a constrained linear least-squares problem, where the objective function is a sum of two least-squares terms and there are box constraints. The original problem is decomposed into two easier least-squares subproblems at each iteration, and to speed up the inner iteration we linearize the relevant subproblem whenever it has no known closed-form solution. We prove the convergence of the resulting algorithm, and apply it to solve some image deblurring problems. Its efficiency is demonstrated, in comparison with Newton-type methods.

Original languageEnglish
Pages (from-to)326-341
Number of pages16
JournalEast Asian Journal on Applied Mathematics
Volume2
Issue number4
DOIs
Publication statusPublished - Nov 2012
Externally publishedYes

Keywords

  • Alternating direction method of multipliers
  • Image processing
  • Linear least-squares problems
  • Linearization

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