Exponential convergence of a distributed divide-and-conquer algorithm for constrained convex optimization on networks

Fuente: arXiv
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Autores principales: Emirov, Nazar, Song, Guohui, Sun, Qiyu
Formato: Preprint
Publicado: 2025
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author Emirov, Nazar
Song, Guohui
Sun, Qiyu
author_facet Emirov, Nazar
Song, Guohui
Sun, Qiyu
contents 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 ($L_2$ distance, quadratic, and entropy) confirm the theory and demonstrate scalability and effectiveness.
format Preprint
id arxiv_https___arxiv_org_abs_2510_01511
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Exponential convergence of a distributed divide-and-conquer algorithm for constrained convex optimization on networks
Emirov, Nazar
Song, Guohui
Sun, Qiyu
Optimization and Control
Distributed, Parallel, and Cluster Computing
Numerical Analysis
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 ($L_2$ distance, quadratic, and entropy) confirm the theory and demonstrate scalability and effectiveness.
title Exponential convergence of a distributed divide-and-conquer algorithm for constrained convex optimization on networks
topic Optimization and Control
Distributed, Parallel, and Cluster Computing
Numerical Analysis
url https://arxiv.org/abs/2510.01511