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GRAPH AND DISTRIBUTED EXTENSIONS OF THE DOUGLAS RACHFORD METHOD.

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Title: GRAPH AND DISTRIBUTED EXTENSIONS OF THE DOUGLAS RACHFORD METHOD.
Authors: BREDIES, KRISTIAN1 kristian.bredies@uni-graz.at, CHENCHENE, ENIS1 enis.chenchene@uni-graz.at, NALDI, EMANUELE2 e.naldi@tu-braunschweig.de
Source: SIAM Journal on Optimization. 2024, Vol. 34 Issue 2, p1569-1594. 26p.
Subjects: Monotone operators, Graph algorithms, Support vector machines, Nonsmooth optimization
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]
Copyright of SIAM Journal on Optimization is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="DE" term="%22Monotone+operators%22">Monotone operators</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+algorithms%22">Graph algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Support+vector+machines%22">Support vector machines</searchLink><br /><searchLink fieldCode="DE" term="%22Nonsmooth+optimization%22">Nonsmooth optimization</searchLink>
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  Data: 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]
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  Data: <i>Copyright of SIAM Journal on Optimization is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Monotone operators
        Type: general
      – SubjectFull: Graph algorithms
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      – SubjectFull: Support vector machines
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              Text: 2024
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