Optimization Problems with Orthogonality Constraints -- from Feasible to Infeasible

：高斌（中国科学院）
：2022-12-01 16:00
：腾讯会议ID：920-253-831（无密码）

报告人：高斌（中国科学院）

时  间：12月1日下午16:00-17:30

地  点：腾讯会议ID：920-253-831（无密码）

内容摘要:

To construct a parallel approach for solving optimization problems with orthogonality constraints is usually regarded as an extremely difficult mission, due to the low scalability of the orthogonalization procedure. However, such demand is particularly huge in some application domains such as material computation. In this talk, we introduce several efficient algorithms including feasible and infeasible methods. Such methods have much lower computational complexity and can also benefit from parallel computing since they are full of BLAS3 operations. In the infeasible algorithm based on a modified augmented Lagrange method, the orthogonalization procedure is only invoked once as the last step. Consequently, the main parts of the proposed algorithms can be parallelized naturally. We establish global subsequence convergence results for our proposed algorithms. Worst-case complexity and local convergence rate are also studied under some mild assumptions. Numerical experiments, including tests under parallel environment, illustrate that our new algorithms attain good performances and high scalability in solving discretized Kohn--Sham total energy minimization problems.

个人简介：

高斌，中国科学院数学与系统科学研究院计算数学所副研究员。2019年毕业于中国科学院数学与系统科学研究院。曾先后赴比利时法语鲁汶大学，德国明斯特大学从事博士后研究。其主要研究兴趣是最优化计算方法的理论，分析和应用，研究内容包括矩阵流形上的优化算法，机器学习中的矩阵填充问题等。曾获中国数学会颁发的钟家庆数学奖。他的多篇论文发表在《SIAM Journal on Optimization》，《SIAM Journal on Scientific Computing》，《SIAM Journal on Matrix Analysis and Applications》等期刊上。

 

联系人：黄文