题  目：Stochastic primal-dual methods for nonconvex constrained optimization

报告人：王  晓

单  位：鹏城实验室

时  间：9月22日10:00

地  点：腾讯709-811-263

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 or when it involves a large number of constraints. In this talk, I will briefly introduce our recent work 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 the function values and gradients of all constraints simultaneously. 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。博士毕业于中科院数学与系统科学研究院计算数学专业。2012.7 至 2021.11 任职于中国科学院大学数学科学学院。研究方向为非线性优化理论与算法。论文发表在包括 SIAM J. Optim., Math. Comput., SIAM J. Imaging Sci., SIAM Numer. Anal.等的国际知名期刊。入选中国科协青年人才托举工程(2018)、中国科学院青年创新促进会会员(2020)、广东省珠江人才计划(2022)、深圳鹏城孔雀特聘计划(2022)。现主持一项国家自然科学基金面上项目、一项鹏城实验室重大攻关项目子课题。目前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。