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Orthogonality-free Approaches for Optimization Problems on Stiefel Manifold
 Orthogonality-free Approaches for Optimization Problems on Stiefel Manifold 教师介绍 本讲教师：袁亚湘 所属学科：理科 人　　气：430 课程介绍 摘要：In this talk, I will discuss some orthogonality-free approaches for optimization problems on Stiefel manifold. Stiefel manifold consists of matrices with orthogonal columns. Optimization problems with orthogonality constraints appear in many important applications such as leading eigenvalues computation, discretized Kohn-Sham total energy minimization, and sparse principal component analysis. We present new algorithms for solving optimization problems on Stieful manifold. These algorithms are based on penalty functions, thus there are no needs to carry out orthogonalization calculations in each iteration. The major computation cost of orthogonality-free algorithms is in the form of matrix-matrix multiplication, which has the advantage of being parallelized easily. Problems with both smooth and nonsmooth objective functions are considered. Theoretical properties of our alrogithms are discussed and numerical experiments are also presented. 报告人简介：袁亚湘现为中国科学院院士、发展中国家科学院院士、巴西科学院通讯院士，美国工业与应用数学会会士、美国数学学会首届会士、国际工业与应用数学联合会当选主席、中国数学会理事长、全国政协常委、中国科协副主席。曾获国家自然科学奖二等奖、首届冯康科学计算奖、TWAS数学奖、陈省身数学奖、苏步青应用数学奖、何梁何利基金科学与技术进步奖等。 袁亚湘院士长期从事运筹学研究并取得了系统成果，在信赖域法、拟牛顿法、非线性共轭梯度法等方法方面做出了重要贡献。在信赖域法方面，给出了著名的Celis-Dennis-Tapia问题的最优性定理；提出并解决了Steihaug-Toint方法的下降估计；和导师Powell合作提出了利用光滑评价函数的约束优化信赖域法；独立提出了一个利用无穷范数罚函数的信赖域法，被国外著名学者推广到整数规划。在拟牛顿法方面，和美国优化专家合作证明了除 DFP 外Broyden 凸簇的所有方法的全局收敛性；提出了一个改进的BFGS方法，发展了非拟牛顿方法。在共轭梯度法方面，和学生合作提出了一个新的共轭梯度法，被国际同行称为“戴袁方法”。