Adaptive Douglas-Rachford splitting algorithm for the sum of two operators

Dao, Minh N.; Phan, Hung M.

Title: Adaptive Douglas-Rachford splitting algorithm for the sum of two operators
Creator: Dao, Minh N.; Phan, Hung M.
Relation: ARC.DP160101537 http://purl.org/au-research/grants/arc/DP160101537
Relation: SIAM Journal on Optimization Vol. 29, Issue 4, p. 2697-2724
Publisher Link: http://dx.doi.org/10.1137/18M121160X
Publisher: Society for Industrial and Applied Mathematics (SIAM)
Resource Type: journal article
Date: 2019
Description: The Douglas-Rachford algorithm is a classical and powerful splitting method for minimizing the sum of two convex functions and, more generally, finding a zero of the sum of two maximally monotone operators. Although this algorithm is well understood when the involved operators are monotone or strongly monotone, the convergence theory for weakly monotone settings is far from being complete. In this paper, we propose an adaptive Douglas-Rachford splitting algorithm for the sum of two operators, one of which is strongly monotone while the other one is weakly monotone. With appropriately chosen parameters, the algorithm converges globally to a fixed point from which we derive a solution of the problem. When one operator is Lipschitz continuous, we prove global linear convergence, which sharpens recent known results.
Subject: Douglas-Rachford algorithm; Fejer monotonicity; global convergence; inclusion problem; linear convergence; Lipschitz continuity; strong monotonicity; weak monotonicity
Identifier: http://hdl.handle.net/1959.13/1413763
Identifier: uon:36669
Identifier: ISSN:1052-6234
Language: eng
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