@Article{JCM-42-5,
author = {Xiao, Nachuan and Xin, Liu},
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 = {<p style="text-align: justify;">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.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2307-m2021-0331},
url = {https://global-sci.com/article/91096/solving-optimization-problems-over-the-stiefel-manifold-by-smooth-exact-penalty-functions}
}