| 报告题目：How to use projected gradient method to globally solve nonconvex trust region subproblem |
报 告 人：夏勇 教授 邀 请 人：张惠珍 | |
工作单位：北京航空航天大学 | |
腾讯会议：243 664 826 | |
报告时间：2022年10月11日（周二）13:30—15:30 | |
报告摘要 | |
The trust region subproblem (TRS) is to minimize a possibly nonconvex quadratic function over a Euclidean ball. There are typically two classes for (TRS), the so-called “easy” and “hard” cases. It may occur even in the “easy case” that the sequence generated by the projected gradient method (PG) starting from any initial point in a nonzero measure feasible set converges locally sublinearly to a saddle point. To our surprise, when applying (PG) to solve a cheap and possibly nonconvex reformulation of (TRS), the generated sequence initialized with a uniformly and randomly generated feasible point converges to the global minimizer of (TRS) with probability one. The local convergence rate is at least linear for the “easy case”, without assuming that we have to possess the information that the “easy case” occurs. We also consider how to use (PG) to globally solve equality-constrained (TRS). | |
报告人简介 | |
夏勇，北京航空航天大学教授，博士生导师，数学科学学院副院长。2002年毕业于北京大学，2007年毕业于中国科学院，师从袁亚湘院士，研究方向为非凸优化，2013年北京青年英才，2018年国家优青，在Math.Program.、SIAMJ.Optim.等期刊上发表SCI论文65篇。中国运筹学会理事、中国运筹学会数学规划分会理事、北京运筹学会理事，中国运筹学会会刊JORSC期刊编委。代表性工作：针对经典二次指派问题提出新模型，被国际国内同行命名为Xia-Yuan线性化；近期在信赖域子问题上继1981年人们完全刻画全局解以来首次建立局部解的充要条件，被誉为“对非线性规划文献的坚实贡献”。 | |
