An accelerated randomized Bregman-Kaczmarz method for strongly convex linearly constraint optimization

Fuente: arXiv
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Auteurs principaux: Tondji, Lionel, Lorenz, Dirk A., Necoara, Ion
Format: Preprint
Publié: 2025
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author Tondji, Lionel
Lorenz, Dirk A.
Necoara, Ion
author_facet Tondji, Lionel
Lorenz, Dirk A.
Necoara, Ion
contents In this paper, we propose a randomized accelerated method for the minimization of a strongly convex function under linear constraints. The method is of Kaczmarz-type, i.e. it only uses a single linear equation in each iteration. To obtain acceleration we build on the fact that the Kaczmarz method is dual to a coordinate descent method. We use a recently proposed acceleration method for the randomized coordinate descent and transfer it to the primal space. This method inherits many of the attractive features of the accelerated coordinate descent method, including its worst-case convergence rates. A theoretical analysis of the convergence of the proposed method is given. Numerical experiments show that the proposed method is more efficient and faster than the existing methods for solving the same problem.
format Preprint
id arxiv_https___arxiv_org_abs_2504_01160
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle An accelerated randomized Bregman-Kaczmarz method for strongly convex linearly constraint optimization
Tondji, Lionel
Lorenz, Dirk A.
Necoara, Ion
Optimization and Control
Numerical Analysis
65F10, 68W20, 90C25
In this paper, we propose a randomized accelerated method for the minimization of a strongly convex function under linear constraints. The method is of Kaczmarz-type, i.e. it only uses a single linear equation in each iteration. To obtain acceleration we build on the fact that the Kaczmarz method is dual to a coordinate descent method. We use a recently proposed acceleration method for the randomized coordinate descent and transfer it to the primal space. This method inherits many of the attractive features of the accelerated coordinate descent method, including its worst-case convergence rates. A theoretical analysis of the convergence of the proposed method is given. Numerical experiments show that the proposed method is more efficient and faster than the existing methods for solving the same problem.
title An accelerated randomized Bregman-Kaczmarz method for strongly convex linearly constraint optimization
topic Optimization and Control
Numerical Analysis
65F10, 68W20, 90C25
url https://arxiv.org/abs/2504.01160