报告人：王晓 教授 中山大学

报告题目：Adaptive directional decomposition methods for nonconvex constrained optimization

时间：2025年12月25日  10:00-12:00

地点：数学楼2-1会议室

摘要：

In this talk, we focus on nonconvex constrained optimization problems with both equality and inequality constraints, covering deterministic and stochastic settings. We propose a novel first-order algorithm framework  that employs a directional  decomposition strategy to balance objective reduction and constraint satisfaction, together with adaptive update of stepsizes and merit parameters. Under certain conditions, the proposed adaptive directional decomposition methods attain an iteration complexity of order \(O(\epsilon^{-2})\) for finding an \(\epsilon\)-KKT point in the deterministic setting. In the stochastic setting, we further develop stochastic variants of approaches and analyze their theoretical properties by leveraging the perturbation theory. We establish the high-probability oracle complexity to find an \(\epsilon\)-KKT point of order \(\tilde O(\epsilon^{-4},\epsilon^{-6})\) (resp. \(\tilde O(\epsilon^{-3}, \epsilon^{-5})\)) for gradient and constraint evaluations, in the absence (resp. presence) of  sample-wise smoothness. To the best of our knowledge, the obtained complexity bounds are comparable to, or improve upon, the state-of-the-art results in the literature.

报告人简介：

王晓，中山大学教授、博士生导师。本科毕业于山东大学数学学院，博士毕业于中国科学院数学与系统科学研究院。先后任职于中国科学院大学数学科学学院、鹏城国家实验室智能计算研究部。研究方向为大规模非凸优化的理论和算法。部分成果发表在SIAM J. Optim.、SIAM J. Numer. Anal.、SIAM J. Imaging Sci.、SIAM J. Matrix. Ana. Appl.、Math. Oper. Res.、Math. Comp.、J. Mach. Learn. Res.等权威期刊。入选国家级青年人才计划、中国科协青年人才托举工程、中国科学院青年创新促进会会员、广东省珠江人才计划青年拔尖人才、中山大学逸仙学者；获聘深圳市鹏城孔雀特聘岗位。曾荣获中国工业与应用数学学会应用数学青年科技奖、中国运筹学会青年科技奖。先后主持国家自然科学基金项目3项、国家级科技计划专项项目课题1项。目前担任中国运筹学会理事。

邀请人：陈志平 教授