深圳技术大学大数据与互联网学院数学系学术报告（五）

报告标题：Stochastic primal-dual methods for nonconvex constrained optimization

报告人：王晓  副研究员（鹏城实验室）

报告时间：2022年11月15日（星期二） 16:00—17:30

报告地点：（腾讯会议）会议号：522-132-808 会议密码：123456

邀请人：王洪  博士

摘要：Nonconvex constrained optimization (NCO) has been one of important research fields in optimization community. A surge of works on NCO in deterministic settings has been proposed in past decades. However, challenges often arise when the exact function information for NCO is hard to access and/or when it involves a large number of constraints. In this talk, I will briefly introduce our recent progress on stochastic approximation methods for NCO. First, I will focus on a class of NCO with a large number of constraints, where we assume it is expensive to go through all constraints to compute their function values and gradients at an iterate. We propose a Stochastic Primal-Dual method (SPD) for this kind of problems. At each iteration, a proximal subproblem based on a stochastic approximation to an augmented Lagrangian (AL) function is solved to update the primal variable, which is then used to update dual variables. Then, I will briefly introduce a STochastic nEsted Primal-dual method (STEP) for nonconvex constrained composition optimization (NCCO), where the objective function has a nest structure. For both algorithms we establish their iteration and sample complexities of SPD to find an approximate solution of original problems.

报告人简介：王晓，鹏城实验室副研究员、博士生导师。2007年本科毕业于山东大学数学基地班，2012年博士毕业于中国科学院数学与系统科学研究院计算数学专业。2012年至2021年任职于中国科学院大学数学科学学院。2021年底加入鹏城实验室。研究方向为非线性优化理论与算法。研究成果发表在SIAM J. Optim., Math. Comput., SIAM J. Imaging Sci., SIAM J. Numer. Anal., J. Sci. Comput.等国际知名期刊。先后入选中国科协第四届青年人才托举工程、中国科学院青年创新促进会第十批会员、广东省珠江人才计划、深圳市鹏城孔雀特聘计划。目前主持国家自然科学基金面上项目、鹏城实验室重大攻关项目子课题，担任中国运筹学会智能工业数据解析与优化专业委员会理事、中国运筹学会数学规划分会青年理事。