地点：学正楼303
邀请人：姜波教授
Abstract:Motivated by recent developments of using cubic regularization to escape saddle points of unconstrained optimization, in this paper we explore its potential in pursuing second-order stationary points of nonconvex constrained optimization whose exact objective function information may be hard to obtain. We first propose an algorithmic framework, named as ICPD, of inexact cubic-regularized primal-dual methods for equality constrained optimization. To update the primal variable at each iteration, we construct a cubic regularized model relying on inexact first- and second-order derivatives of the objective function together with information of constraint functions. By allowing an inexact solutions to each subproblem under certain conditions, we establish the iteration complexities of ICPD to find an $\epsilon$-approximate first- and second-order stationary point, respectively. We then consider a stochastic variant algorithm SCPD for equality constrained optimization whose objective takes an expectation form. Through a proper sampling strategy to calculate stochastic gradients and Hessians, we address the oracle complexities of SCPD to reach approximate stationary points with high probability. We also investigate the behavior of the standard gradient descent when solving each subproblem with a random perturbation. We provide a detailed analysis on how to fulfill the required conditions on an inexact subproblem solution with high probability at each iteration. Additionally, we present an analysis of an adaptive variant of ICPD which updates penalty parameters dynamically and discuss the applicability of adaptive cubic regularization parameters.
个人简介：王晓，鹏城国家实验室智能计算研究部副研究员、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年至2021年任职于中国科学院大学网赌
。研究方向包括物理约束等复杂约束模型的近似算法理论、稀疏正则化算法理论、AI近似数值模拟计算的应用分析等。部分成果发表在SIAM系列期刊、Math. Comput.、J. Sci. Comput.、J. Mach. Learn. Res.等权威期刊。入选国家级青年人才计划、荣获第八届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三项、国家级科技计划专项项目课题一项。
