@Article{JCM-42-1246, author = {Xiao , Nachuan and Liu , Xin}, title = {Solving Optimization Problems over the Stiefel Manifold by Smooth Exact Penalty Functions}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {5}, pages = {1246--1276}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2307-m2021-0331}, url = {http://global-sci.org/intro/article_detail/jcm/23277.html} }