鞍点问题的随机预条件Douglas-Rachford分裂方法

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2025-08-12 DOI:10.1137/23m1622490

Yakun Dong, Kristian Bredies, Hongpeng Sun

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引用次数: 0

摘要

SIAM数值分析杂志，第63卷，第4期，1691-1728页，2025年8月。摘要。本文提出并研究了一种求解具有可分离对偶变量的鞍点问题的随机松弛预条件Douglas-Rachford分裂方法。证明了一类凹凸非光滑鞍点问题的迭代序列在Hilbert空间中的几乎肯定收敛性。我们还给出了关于受限原对偶间隙函数期望的遍历序列的次线性收敛速率。数值实验表明，本文提出的随机松弛预条件Douglas-Rachford分裂方法具有较高的效率。

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A Stochastic Preconditioned Douglas–Rachford Splitting Method for Saddle-Point Problems

SIAM Journal on Numerical Analysis, Volume 63, Issue 4, Page 1691-1728, August 2025.
Abstract. In this article, we propose and study a stochastic and relaxed preconditioned Douglas–Rachford splitting method to solve saddle-point problems that have separable dual variables. We prove the almost sure convergence of the iteration sequences in Hilbert spaces for a class of convex-concave and nonsmooth saddle-point problems. We also provide the sublinear convergence rate for the ergodic sequence concerning the expectation of the restricted primal-dual gap functions. Numerical experiments show the high efficiency of the proposed stochastic and relaxed preconditioned Douglas–Rachford splitting methods.

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.