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arXiv · 2212.13001

A stochastic preconditioned Douglas-Rachford splitting method for saddle-point problems

Yakun Dong·Kristian Bredies·Hongpeng Sun
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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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Yakun Dong, Kristian Bredies, Hongpeng Sun. 2022-12-26. A stochastic preconditioned Douglas-Rachford splitting method for saddle-point problems. https://arxiv.org/abs/2212.13001

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