报告问题：Tight Error Bounds for Nonnegative Orthogonality Constraints and Exact Penalties
报告时间：2023年4月14日 10:00
报告所在：#腾讯聚会：175-148-585
报 告 人：张在坤 博士
主 持 人：寇彩霞 副教授
报告摘要：
For the intersection of the Stiefel manifold and the set of nonnegative matrices in R^{n×r}, 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.
报告人简介：
张在坤，博士，香港理工大学应用数学系助理教授。2007 年本科结业于吉林大学，2012 年博士结业于中国科学院。主要研究无导数优化要领，基于不准确信息的要领，随机化要领等。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，研究事情揭晓于 Mathematical Programming, SIAM Journal on Optimization, and SIAM Journal on Scientific Computing 等杂志。
