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

Renato D.C. Monteiro(monteiro***at***isye.gatech.edu)
Chee-Khian Sim(chee-khian.sim***at***port.ac.uk)

Abstract: This paper considers the relaxed Peaceman-Rachford (PR) splitting method for fi nding 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, convergence of the iterates, as well as pointwise and ergodic convergence rate, are established for the above 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.

Keywords: Relaxed Peaceman-Rachford splitting method; strongly monotone operators; non-Euclidean hybrid proximal extragradient framework

Category 1: Convex and Nonsmooth Optimization

Citation: Submitted

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Entry Submitted: 11/03/2016
Entry Accepted: 11/03/2016
Entry Last Modified: 11/03/2016

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