报告主题：Parallelizable Algorithms for Optimization Problems with Orthogonality Constraints
报告人：刘歆 副研究员 （中国科学院数学与系统研究院）
报告时间：2018年12月30日（周日）16：00
报告地点：校本部G508
邀请人：白延琴 教授
主办部门：太阳成集团tyc33455数学系
报告摘要：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 propose two infeasible algorithms, based on augmented Lagrangian penalty function, for solving optimization problems with orthogonality constraints. Different with the classic augmented Lagrangian method, our algorithm supdate both the prime variables and the dual variables by new strategies. The orthogonalization procedure is only invoked once as the last step of the above mentioned two algorithms. Consequently, the main parts of the set two 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 attaing ood performances high scalability in solving discretized Kohn-Shamtotal energy minimization problems.
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