A strictly contractive Peaceman-Rachford splitting method with logarithmic-quadratic proximal regularization for convex programming

Min Li, Xiaoming YUAN

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

Recently, a strictly contractive Peaceman-Rachford splitting method (PRSM) was proposed for a separable convex minimization model whose variables are subject to some linear constraints and two additional generic constraints. In general, the strictly contractive PRSM requires to solve two constrained minimization subproblems at each iteration. In this paper, we consider the case where the additional constraints on variables are positive orthants and apply the well-developed logarithmicquadratic proximal (LQP) regularization to regularize the subproblems of the strictly contractive PRSM. A new algorithm in combination with the strictly contractive PRSM and the LQP regularization is thus proposed. The new algorithm only needs to solve two unconstrained subproblems at each iteration. An inexact version allowing the unconstrained subproblems to be solved approximately subject to certain inexactness criterion is also studied. We prove the global convergence and establish a worst-case convergence rate measured by the iteration complexity for both the exact and inexact versions of the new algorithm.

Original languageEnglish
Pages (from-to)842-858
Number of pages17
JournalMathematics of Operations Research
Volume40
Issue number4
DOIs
Publication statusPublished - Nov 2015

Scopus Subject Areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

User-Defined Keywords

  • Convergence rate
  • Convex programming
  • Iteration complexity
  • Logarithmic-quadratic proximal regularization
  • Peaceman-Rachford splitting method

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