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北京航空航天大学夏勇教授学术报告通知
发布人:蔡易  发布时间:2022-07-01   浏览次数:10

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:202274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