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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Bibliographic Details
Published in:	Expositiones mathematicae Vol. 43; no. 6; p. 125740
Main Authors:	Emirov, Nazar, Song, Guohui, Sun, Qiyu
Format:	Journal Article
Language:	English
Published:	Elsevier GmbH 01.12.2025
Subjects:	Constrained convex optimization on network Distributed and decentralized algorithm Divide and conquer algorithm secondary Constrained convex optimization on network Distributed and decentralized algorithm Divide and conquer algorithm primary
ISSN:	0723-0869
Online Access:	Get full text
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Summary:	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.
ISSN:	0723-0869
DOI:	10.1016/j.exmath.2025.125740