A Peaceman–Rachford Splitting Method with Monotone Plus Skew-Symmetric Splitting for Nonlinear Saddle Point Problems

Weiyang DING, Kwok Po NG, Wenxing Zhang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This paper is devoted to solving the linearly constrained convex optimization problems by Peaceman–Rachford splitting method with monotone plus skew-symmetric splitting on KKT operators. This approach generalizes the Hermitian and skew-Hermitian splitting method, an unconditionally convergent algorithm for non-Hermitian positive definite linear systems, to the nonlinear scenario. The convergence of the proposed algorithm is guaranteed under some mild assumptions, e.g., the strict convexity on objective functions and the consistency on constraints, even though the Lions–Mercier property is not fulfilled. In addition, we explore an inexact version of the proposed algorithm, which allows solving the subproblems approximately with some inexactness criteria. Numerical simulations on an image restoration problem demonstrate the compelling performance of the proposed algorithm.

Original languageEnglish
Pages (from-to)763-788
Number of pages26
JournalJournal of Scientific Computing
Volume81
Issue number2
DOIs
Publication statusPublished - 1 Nov 2019

Scopus Subject Areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Contraction
  • Hermitian and skew-Hermitian splitting method
  • Image restoration
  • Inexact method
  • Parallel computing
  • Peaceman–Rachford splitting method
  • Saddle point problem

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