报告人：夏勇教授

报告题目：How to use projected gradient method to globally solve nonconvex trust region subproblem

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).

报告时间：2022年7月4号上午09:30-12:00

报告形式：腾讯会议；会议号：664 4945 0076

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.、SIAM J. Optim.等期刊发表SCI论文62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，被中、美、加、德、意、西班牙等国际国内同行命名为Xia-Yuan线性化，其松弛被称为Xia-Yuan界；近期在信赖域子问题上继1981年人们完全刻画全局解39年来首次建立局部解的充要条件，终结了巴西科学院院士Martínez刻画的必要条件和充分条件之间存在了26年的间隙，被誉为“对非线性规划文献的坚实贡献”。