In this article, we propose and study a stochastic preconditioned Douglas-Rachford splitting method to solve saddle-point problems which have separable dual variables. We prove the almost sure convergence of the iteration sequences in Hilbert spaces for a class of convexconcave and nonsmooth saddle-point problems. We also provide the sublinear convergence rate for the ergodic sequence with respect to the expectation of the restricted primal-dual gap functions. Numerical experiments show the high efficiency of the proposed stochastic preconditioned Douglas-Rachford splitting methods.

翻译：本文提出并研究了一种随机预处理道格拉斯-拉赫福德分裂方法，用于求解具有可分离对偶变量的鞍点问题。我们证明了在希尔伯特空间中，对于一类凸凹且非光滑的鞍点问题，迭代序列几乎必然收敛。我们还给出了关于受限原始-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，所提出的随机预处理道格拉斯-拉赫福德分裂方法具有高效性。