论文标题
鞍点问题的随机预处理道格拉斯 - 拉赫福德分裂方法
A stochastic preconditioned Douglas-Rachford splitting method for saddle-point problems
论文作者
论文摘要
在本文中，我们提出并研究了一种随机且放松的预处理道格拉斯 - 拉赫福德分裂方法，以解决具有可分离的双重变量的鞍点问题。我们证明了希尔伯特空间中迭代序列的几乎确定的收敛性，用于一类凸孔和非平滑鞍点问题。我们还提供有关限制性原始偶差函数的期望的厄贡序列的额定性收敛速率。数值实验表明，提出的随机和松弛的预处理道格拉斯 - 拉赫福德分裂方法的高效率。
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.
