数学系2023年系列学术报告（二）

报告标题：Tight error bounds for nonnegative orthogonality constraints and exact penalties

报告人：张在坤  助理教授（香港理工大学）

报告时间：2023年4月13日（星期四） 15:00—16:00

报告地点：（腾讯会议）会议号：291-596-160  会议密码：123456

邀请人：王洪博士

摘要：For the intersection of the Stiefel manifold and the set of nonnegative matrices in R^{nxr}, we present global and local error bounds with easily computable residual functions and explicit coefficients. Moreover, we show that the error bounds cannot be improved except for the coefficients, which explains why two square-root terms are necessary in the bounds when 1<r<n for the nonnegativity and orthogonality, respectively. The error bounds are applied to penalty methods for minimizing a Lipschitz continuous function with nonnegative orthogonality constraints. Under only the Lipschitz continuity of the objective function, we prove the exactness of penalty problems that penalize the nonnegativity constraint, or the orthogonality constraint, or both constraints. Our results cover both global and local minimizers. (This is joint work with Professor Xiaojun Chen and Mr. Yifan He from The Hong Kong Polytechnic University.)

报告人简介：张在坤博士 2007 年本科毕业于吉林大学，2012 年博士毕业于中国科学院， 目前任香港理工大学应用数学系助理教授。张在坤博士主要研究主要研究无导数优化方法，基于不精确信息的方法，随机化方法等。他主持香港－法国 PROCORE 研究项目一项，香港研究资助局 ECS 项目一项，GRF 项目两项，研究工作发表于 Mathematical Programming, SIAM Journal on Optimization, and SIAM Journal on Scientific Computing 等杂志。