Non-Convergence Analysis of
Randomized Direct Search
报告专家：张在坤 教授（中山大学）
报告时间：11月12日（周三）10:30-11:30
报告地点：数学学院西303报告厅
报告摘要：
Direct search is a popular method in derivative-free optimization. Randomized direct search has attracted increasing attention in recent years due to both its practical success and theoretical appeal. It is proved to converge under certain conditions at the same global rate as its deterministic counterpart, but the cost per iteration is much lower, leading to significant advantages in practice. However, a fundamental question has been lacking a systematic theoretical investigation: when will randomized direct search fail to converge? We answer this question by establishing the non-convergence theory of randomized direct search. We prove that randomized direct search fails to converge if the searching set is probabilistic ascent. Our theory does not only deepen our understanding of the behavior of the algorithm, but also clarifies the limit of reducing the cost per iteration by randomization, and hence provides guidance for practical implementations of randomized direct search.
This is a joint work with Cunxin Huang, a Ph.D. student funded by the Hong Kong Ph.D. Fellowship Scheme.
专家简介：
张在坤 2007 年本科毕业于吉林大学，2012 年博士毕业于中国科学院，目前为中山大学数学学院教授、博士生导师、逸仙优秀学者。他的主要研究兴趣为最优化理论与算法，特别是无导数方法、基于不精确信息的方法、随机化方法等。他的代表作发表于 Math. Program.、 SIAM J. Optim.、SIAM J. Sci. Comput. 等杂志。张在坤现主持国家自然科学基金面上项目一项，曾主持香港研究资助局 ECS/GRF 项目五项，参与科技部国家重点研发计划两项，并于 2023 年入选国家级青年人才计划。2024 年，张在坤的团队被授予中国运筹学会科学技术奖“运筹应用奖”。
邀请人：王皓
