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GRAPH AND DISTRIBUTED EXTENSIONS OF THE DOUGLAS RACHFORD METHOD.
- Source :
-
SIAM Journal on Optimization . 2024, Vol. 34 Issue 2, p1569-1594. 26p. - Publication Year :
- 2024
-
Abstract
- In this paper, we propose several graph-based extensions of the Douglas-Rachford splitting (DRS) method to solve monotone inclusion problems involving the sum of N maximal monotone operators. Our construction is based on the choice of two nested graphs, to which we associate a generalization of the DRS algorithm that presents a prescribed structure. The resulting schemes can be understood as unconditionally stable frugal resolvent splitting methods with minimal lifting in the sense of Ryu [Math. Program., 182 (2020), pp. 233-273] as well as instances of the (degenerate) preconditioned proximal point method, which provides robust convergence guarantees. We further describe how the graph-based extensions of the DRS method can be leveraged to design new fully distributed protocols. Applications to a congested optimal transport problem and to distributed support vector machines show interesting connections with the underlying graph topology and highly competitive performances with state-of-the-art distributed optimization approaches. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10526234
- Volume :
- 34
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 178370479
- Full Text :
- https://doi.org/10.1137/22M1535097