SOLVING OPTIMIZATION PROBLEMS OVER THE STIEFEL MANIFOLD BY SMOOTH EXACT PENALTY FUNCTIONS  

作　　者：Nachuan Xiao Xin Liu 

机构地区：[1]The Institute of Operations Research and Analytics,National University of Singapore,Singapore [2]State Key Laboratory of Scientific and Engineering Computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,and University of Chinese Academy of Sciences,China

出　　处：《Journal of Computational Mathematics》2024年第5期1246-1276,共31页计算数学（英文）

基　　金：the National Natural Science Foundation of China(Grant Nos.12125108,11971466,12288201,12021001,11991021);the Key Research Program of Frontier Sciences,Chinese Academy of Sciences(Grant No.ZDBS-LY-7022).

摘　　要：In this paper,we present a novel penalty model called ExPen for optimization over the Stiefel manifold.Different from existing penalty functions for orthogonality constraints,ExPen adopts a smooth penalty function without using any first-order derivative of the objective function.We show that all the first-order stationary points of ExPen with a sufficiently large penalty parameter are either feasible,namely,are the first-order stationary points of the original optimization problem,or far from the Stiefel manifold.Besides,the original problem and ExPen share the same second-order stationary points.Remarkably,the exact gradient and Hessian of ExPen are easy to compute.As a consequence,abundant algorithm resources in unconstrained optimization can be applied straightforwardly to solve ExPen.

关 键 词：Orthogonality constraint Stiefel manifold Penalty function 

分 类 号：O174[理学—数学]