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

Speaker: 孙鸿鹏（中国人民大学）

Time: 2025 Jul.11th 16:00-17:00
Location: R1610, SIMIS

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. This is a joint work with Yakun Dong and Kristian Bredies.

About Speaker:
孙鸿鹏，中国人民大学教授，博导。2012年博士毕业于中国科学院数学与系统科学研究院，2012-2014奥地利格拉茨大学博后，研究方向反问题和图像处理。现主持国家自然科学基金面上项目、北京市自然科学基金重点项目子课题、曾主持德国洪堡基金等项目。在相关领域期刊发表论文多篇，包括权威期刊如SIAM J. Numer. Anal., IP， SIAM SISC， SIAM MMS等。