A proximal strictly contractive Peaceman–Rachford splitting method for convex programming with applications to imaging

Xinxin Li, Xiaoming YUAN

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

Abstract

A strictly contractive Peaceman–Rachford splitting method was proposed recently for solving separable convex programming problems. In this paper we further discuss a proximal version of this method, where a subproblem at each iteration is regularized by a proximal point term. The resulting regularized subproblem thus may have closed-form or easily computable solutions, especially in some interesting applications such as a class of sparse and low-rank optimization models. We establish the worst-case convergence rate measured by the iteration complexity in both the ergodic and nonergodic senses for the new algorithm. Some applications arising in image processing are tested to demonstrate the efficiency of the new algorithm.

Original languageEnglish
Article numberA020
Pages (from-to)1332-1365
Number of pages34
JournalSIAM Journal on Imaging Sciences
Volume8
Issue number2
DOIs
Publication statusPublished - 24 May 2015

Scopus Subject Areas

  • Mathematics(all)
  • Applied Mathematics

User-Defined Keywords

  • Contraction
  • Convergence rate
  • Convex programming
  • Image processing
  • Peaceman–Rachford splitting method

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