学术报告报告题目：A Class of Smooth Exact Penalty Function Methods for Optimization Problems with Orthogonality Constraints
报 告 人：刘歆 副研究员(中科院计算数学研究所)
报告时间：2019年9 月18 日（星期三）下午2:30-3:30
报告地点：3号楼6楼会议室
邀 请 人：贲树军博士、潘少华教授
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数学学院
2019年9月16日
报告摘要：
Updating the augmented Lagrangian multiplier by closed-form expression yields efficient first-order infeasible approach for optimization problems with orthogonality constraints. Hence, parallelization becomes tractable in solving this type of problems. Inspired by this closed-form updating scheme, we propose an exact penalty function model with compact convex constraints (PenC). We show its equivalence to optimization problems with orthogonality constraints under mild condition. Based on PenC, we first propose a first-order algorithm called PenCF and establish its global convergence and local linear convergence rate under some mild assumptions. If the computation and storage of Hessian is achievable, and we pursue high precision solution and fast local convergence rate, a second-order approach called PenCS is proposed under the same penalty function. To avoid expensive calculation or solving a hard subproblem in computing the Newton step, we propose a new strategy to do it approximately which leads to quadratic convergence theoretically. Moreover, the main iterations of both PenCF and PenCS are orthonormalization-free and hence parallelizable. Numerical experiments illustrate that PenCF is comparable with existing first-order methods including the existent infeasible approaches. Furthermore, PenCS shows its stability and high efficiency in obtain high precision solution in comparing with the existent second-order methods.
报告人简介：
刘歆，中科院计算数学研究所副研究员，本科毕业于北京大学数学科学学院，博士毕业于中科院数学与系统科学研究院，师从袁亚湘院士，先后在德国ZIB研究所、莱斯大学、纽约大学访问。
主要从事正交约束优化的数值算法、非线性最小二乘的理论与算法、矩阵计算和深度学习等方面的研究，曾获中国科学院数学与系统科学研究院“陈景润未来之星”计划奖、国家自然科学基金委国家优秀青年科学基金资助、中国运筹学会青年科技奖、中国科学院北京分院“启明星”优秀人才奖、中国数学会计算数学分会青年创新提名奖等；是Mathematical Programming Computation期刊的编委，在Mathematical Programming，SIAM Journal on Numerical Analysis，SIAM Journal on Matrix Analysis and Applications，SIAM Journal on Scientific Computing，SIAM Journal on Optimization，Mathematics of Operations Research，IEEE Transactions on Information Theory等国际顶级期刊上发表论文10余篇。