学术报告 报告题目: Stochastic nested primal-dual method for nonconvex constrained composition optimization
报 告 人: 王晓 教授
报告时间: 2025年3月27日（星期四）3:45-4:30
地 点：37号楼3A02
邀 请 人: 潘少华教授
数学学院
2025年3月20日
报告摘要：In this talk we focus the nonconvex constrained composition optimization, in which the objective contains a composition of two expected-value functions whose accurate information is normally expensive to calculate. We propose a STochastic nEsted Primal-dual (STEP) method for such problems. In each iteration, with an auxiliary variable introduced to track the inner layer function values we compute stochastic gradients of the nested function using a subsampling strategy. To alleviate difficulties caused by possibly nonconvex constraints, we construct a stochastic approximation to the linearized augmented Lagrangian function to update the primal variable, which further motivates to update the dual variable in a weighted-average way. Moreover, to better understand the asymptotic dynamics of the update schemes we consider a deterministic continuous-time system from the perspective of ODE. We analyze the KKT measure at the output by the STEP method with constant parameters and establish its iteration and sample complexities to find an $\epsilon$-stationary point, ensuring that expected stationarity, feasibility as well as complementary slackness are below accuracy $\epsilon$. To leverage the benefit of the (near) initial feasibility in the STEP method, we propose a two-stage framework incorporating a feasibility-seeking phase, aiming to locate a nearly feasible initial point. Moreover, to enhance the adaptivity of the STEP algorithm, we propose an adaptive variant by adaptively adjusting its parameters, along with a complexity analysis. Numerical results on a risk-averse portfolio optimization problem and orthogonal nonnegative matrix decomposition reveal the effectiveness of the proposed algorithms.
报告人简介：王晓，中山大学计算机学院教授、（计算数学）博士生导师。本科毕业于山东大学数学基地班，博士毕业于中国科学院数学与系统科学研究院。2012.7至2025.3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.、J. Sci. Comput.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；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、中国科学院大学领雁奖银奖。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。