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:在本篇文章中,我们提出并研究一种具有挑战性的先决条件道格拉斯-拉赫福德分裂法,以解决具有可分离的双重变量的马鞍点问题。我们证明希尔伯特空域的迭代顺序几乎可以肯定地融合成一类紧凑和非摩擦的马鞍点问题。我们还提供了离子序列的亚线趋同率,以适应对限制的原始-双重差距功能的期望。数字实验表明,拟议的道格拉斯-拉赫福德分离方法具有很高的效率。