Peaceman–Rachford splitting for a class of nonconvex optimization problems

Guoyin Li, Tianxiang Liu, Ting Kei Pong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

14 Citations (Scopus)

Abstract

We study the applicability of the Peaceman–Rachford (PR) splitting method for solving nonconvex optimization problems. When applied to minimizing the sum of a strongly convex Lipschitz differentiable function and a proper closed function, we show that if the strongly convex function has a large enough strong convexity modulus and the step-size parameter is chosen below a threshold that is computable, then any cluster point of the sequence generated, if exists, will give a stationary point of the optimization problem. We also give sufficient conditions guaranteeing boundedness of the sequence generated. We then discuss one way to split the objective so that the proposed method can be suitably applied to solving optimization problems with a coercive objective that is the sum of a (not necessarily strongly) convex Lipschitz differentiable function and a proper closed function; this setting covers a large class of nonconvex feasibility problems and constrained least squares problems. Finally, we illustrate the proposed algorithm numerically.
Original languageEnglish
Pages (from-to)407-436
Number of pages30
JournalComputational Optimization and Applications
Volume68
Issue number2
DOIs
Publication statusPublished - 1 Nov 2017

Keywords

  • Feasibility problems
  • Global convergence
  • Nonconvex optimization problems
  • Peaceman–Rachford splitting

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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