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Complexity of the relaxed Peaceman-Rachford splitting method for the sum of two maximal strongly monotone operators

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This paper considers the relaxed Peaceman-Rachford (PR) splitting method for finding an approximate solution of a monotone inclusion whose underlying operator consists of the sum of two maximal strongly monotone operators. Using general results obtained in the setting of a non-Euclidean hybrid proximal extragradient framework, we extend a previous convergence result on the iterates generated by the relaxed PR splitting method, as well as establish new pointwise and ergodic convergence rate results for the method whenever an associated relaxation parameter is within a certain interval. An example is also discussed to demonstrate that the iterates may not converge when the relaxation parameter is outside this interval.
Original languageEnglish
Pages (from-to)763-790
Number of pages28
JournalComputational Optimization and Applications
Volume70
Issue number3
Early online date20 Mar 2018
DOIs
Publication statusPublished - 1 Jul 2018

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