报告地点：行健楼学术活动室526
邀请人：徐玲玲教授
摘要：Randomized iterative methods have gained recent interest in machine learning and signal processing for solving large-scale linear systems. One such example is the randomized Douglas–Rachford (RDR) method, which updates the iterate by reflecting it through two randomly selected hyperplanes and taking a convex combination with the current point. In this talk, we enhance RDR by introducing improved sampling strategies and an adaptive heavy-ball momentum scheme. Specifically, we incorporate without-replacement and volume sampling into RDR, and establish stronger convergence guarantees compared to conventional i.i.d. sampling. Furthermore, we develop an adaptive momentum mechanism that dynamically adjusts step sizes and momentum parameters based on previous iterates, and prove that the resulting method achieves linear convergence in expectation with improved convergence bounds. Numerical experiments demonstrate that the enhanced RDR method consistently outperforms the original version, providing substantial practical benefits across a range of problem settings. The arXiv link: //arxiv.org/abs/2506.10261.
报告人简介：谢家新，北京航空航天大学网赌
副教授，博士生导师，2017年获湖南大学计算数学博士学位，随后进入中国科学院数学与系统科学研究院从事博士后研究，2019年入职北京航空航天大学网赌
。研究兴趣为数据科学中的数学问题，特别是随机迭代法及其加速技术。已在SIMAX, SIOPT, IJM, JCM, COAP等期刊发表论文多篇。现为中国运筹学会算法软件及应用分会理事，中国运筹学会数学规划分会青年理事。
