Backward-Forward-Reflected-Backward Splitting for Three Operator Monotone Inclusions

Janosch Rieger and Matthew K. Tam

Applied Mathematics and Computation, 2020, vol. 381, issue C

Abstract: In this work, we propose and analyse two splitting algorithms for finding a zero of the sum of three monotone operators, one of which is assumed to be Lipschitz continuous. Each iteration of these algorithms require one forward evaluation of the Lipschitz continuous operator and one resolvent evaluation of each of the other two operators. By specialising to two operator inclusions, we recover the forward-reflected-backward and the reflected-forward-backward splitting methods as particular cases. The inspiration for the proposed algorithms arises from interpretations of the aforementioned reflected splitting algorithms as discretisations of the continuous-time proximal point algorithm.

Keywords: operator splitting; monotone operators; dynamical systems (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:381:y:2020:i:c:s0096300320302174

DOI: 10.1016/j.amc.2020.125248

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