Exponential convergence of a distributed divide-and-conquer algorithm for constrained convex optimization on networks
We propose a divide-and-conquer (DAC) algorithm for constrained convex optimization over networks, where the global objective is the sum of local objectives attached to individual agents. The algorithm is fully distributed: each iteration solves local subproblems around selected fusion centers and c...
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| Vydané v: | Expositiones mathematicae Ročník 43; číslo 6; s. 125740 |
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| Jazyk: | English |
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Elsevier GmbH
01.12.2025
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| ISSN: | 0723-0869 |
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| Abstract | We propose a divide-and-conquer (DAC) algorithm for constrained convex optimization over networks, where the global objective is the sum of local objectives attached to individual agents. The algorithm is fully distributed: each iteration solves local subproblems around selected fusion centers and coordinates only with neighboring fusion centers. Under standard assumptions of smoothness, strong convexity, and locality on the objective function, together with polynomial growth conditions on the underlying graph, we establish exponential convergence of the DAC iterations and derive explicit bounds for both exact and inexact local solvers. Numerical experiments on three representative losses (L2 distance, quadratic, and entropy) confirm the theory and demonstrate scalability and effectiveness. |
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| AbstractList | We propose a divide-and-conquer (DAC) algorithm for constrained convex optimization over networks, where the global objective is the sum of local objectives attached to individual agents. The algorithm is fully distributed: each iteration solves local subproblems around selected fusion centers and coordinates only with neighboring fusion centers. Under standard assumptions of smoothness, strong convexity, and locality on the objective function, together with polynomial growth conditions on the underlying graph, we establish exponential convergence of the DAC iterations and derive explicit bounds for both exact and inexact local solvers. Numerical experiments on three representative losses (L2 distance, quadratic, and entropy) confirm the theory and demonstrate scalability and effectiveness. |
| ArticleNumber | 125740 |
| Author | Sun, Qiyu Song, Guohui Emirov, Nazar |
| Author_xml | – sequence: 1 givenname: Nazar surname: Emirov fullname: Emirov, Nazar email: nazaremirov@gmail.com organization: Department of Mathematics, University of Central Florida, Orlando, FL 32816, United States of America – sequence: 2 givenname: Guohui surname: Song fullname: Song, Guohui email: gsong@odu.edu organization: Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, United States of America – sequence: 3 givenname: Qiyu orcidid: 0000-0002-0341-313X surname: Sun fullname: Sun, Qiyu email: qiyu.sun@ucf.edu organization: Department of Mathematics, University of Central Florida, Orlando, FL 32816, United States of America |
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| Cites_doi | 10.1016/j.acha.2017.07.007 10.1016/j.acha.2023.101623 10.1137/16M1084316 10.1109/LCSYS.2019.2923078 10.1090/S0002-9947-06-03841-4 10.1103/PhysRev.106.620 10.1016/j.automatica.2017.07.003 10.1016/j.arcontrol.2019.05.006 10.1090/S0025-5718-1984-0758197-9 10.1007/s10444-013-9314-3 10.1137/14096668X 10.1109/TAC.2019.2912494 10.1109/TAC.2014.2308612 10.1007/s00365-010-9121-8 10.1137/15M1049294 10.1090/S0002-9947-07-04303-6 10.1007/978-3-319-00825-7 10.1016/j.laa.2006.11.003 10.1109/TII.2012.2219061 10.1016/j.jfa.2018.09.014 10.1023/A:1007379606734 10.1109/TAC.2008.2009515 10.1561/2200000016 |
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| Keywords | secondary Constrained convex optimization on network Distributed and decentralized algorithm Divide and conquer algorithm primary |
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| SubjectTerms | Constrained convex optimization on network Distributed and decentralized algorithm Divide and conquer algorithm |
| Title | Exponential convergence of a distributed divide-and-conquer algorithm for constrained convex optimization on networks |
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