报告人：姜波（南京师范大学）

报告时间：2021年6月26日 9：00-10：00

报告地点：数学楼307

报告摘要：Optimization with nonnegative orthogonality constraints has wide applications in machine learning and data sciences. It is NP-hard due to some combinatorial properties of  the constraints. We first propose an equivalent optimization formulation with nonnegative and multiple spherical constraints and an additional single  nonlinear constraint. Various constraint qualifications, the first- and second-order optimality conditions of the equivalent formulation are discussed. By establishing a local error bound of the feasible set, we design a class of (smooth) exact penalty models via keeping the nonnegative and multiple spherical constraints. The penalty models are exact if the penalty parameter is sufficiently large other than going to infinity. A practical penalty algorithm with postprocessing is then developed to approximately solve a series of subproblems with nonnegative and multiple spherical constraints.  We study the asymptotic convergence and establish that any limit point is a weakly stationary point of the original problem and becomes a stationary point under some additional mild conditions.  Extensive numerical results on the projection problem, orthogonal nonnegative matrix factorization problems and the K-indicators model show the effectiveness of our proposed approach.

报告人简介：姜波，南京师范大学数学科学学院副教授、硕士生导师。2013年博士毕业于中国科学院数学与系统科学研究院。2013年09月-2014年03月在美国明尼苏达大学（双城），2017年09-2018年09月在香港理工大学应用数学系做博士后研究。主要研究兴趣为：非线性优化算法与理论，特别是带有正交约束的优化问题及其应用。目前主持国家自然科学基金面上项目1项。曾主持中国科协青年托举工程项目1项、国家自然科学基金青年项目1项和江苏省青年基金项目1项。现为中国运筹学会数学规划分会的青年理事。在Math. Program., SIAM J. Optim, SIAM J. Sci. Comput., IEEE T. Image Process.等杂志发表数篇学术论文。

邀请人：陈中文