潘少华教授受邀进行讲座

发布时间: 2023-11-30 15:42:00

题目：Calmness of partial perturbation to composite rank constraint systems and its applications to combinatorial optimization

报告人：潘少华教授

时间：2023-11-29 15:00-16:00

地点：腾讯会议：656-4902-4546

报告人简介：

华南理工大学数学学院教授、博士生导师。现任中国运筹学会理事和中国运筹学会数学规划分会常务理事。研究方向：低秩稀疏优化问题、锥约束优化与互补问题的理论与算法研究、非凸非光滑复合优化的算法研究。主持国家多项国家自科基金，在国际重要优化和计算刊物Mathematical Programming, SIAM Journal on Optimization, SIAM Journal on Control and Optimization, SIAM Journal on Scientific Computing, IMAJournal on Numerical Analysis 等杂志发表论文50余篇，2019年荣获广东省自然科学二等奖。

讲座摘要：

This talk concerns the calmness of a partial perturbation to the composite rank constraint system, an intersection of the rank constraint set and a general closed set, which is shown to be equivalent to a local Lipschitzian error bound and also a global Lipschitzianerror bound under a certain compactness condition, Based on its lifted formulation, we derive two criteria for identifying those closed sets such that the associated partial perturbation possesses the calmness, and provide a collection of examples to demonstrate that the criteria are satistied by common nonnegative and positive semidefinite rank constraint sets. Then, we apply the calmness of this class of partial perturbation to achieve several global exact penalties for rank constrained optimization, and employ one of them to propose a continuous relaxation approach to a class of unconstrained binary polynomial programs. Numerical tests on 184 instances demonstrate the efficiency of the proposed method, which can solve the problem of 20000 variables in $10$ minutes on an ordinary workstation and yields an upper bound to the best with a relative error at most 2.428%.

主办单位：华南师范大学数学科学学院，机器学习与最优化计算实验室

协办单位：广东省青年科学家协会，广东省计算数学学会