A stochastic preconditioned Douglas-Rachford splitting method for saddle-point problems
Optimization and Control
2024-10-01 v3 Numerical Analysis
Numerical Analysis
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.
Cite
@article{arxiv.2212.13001,
title = {A stochastic preconditioned Douglas-Rachford splitting method for saddle-point problems},
author = {Yakun Dong and Kristian Bredies and Hongpeng Sun},
journal= {arXiv preprint arXiv:2212.13001},
year = {2024}
}