@Article{CSIAM-AM-2-3,
author = {Wang, Lei and Gao, Bin and Xin, Liu},
title = {Multipliers Correction Methods for Optimization Problems over the Stiefel Manifold},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2021},
volume = {2},
number = {3},
pages = {508--531},
abstract = {<p style="text-align: justify;">We propose a class of multipliers correction methods to minimize a differentiable function over the Stiefel manifold. The proposed methods combine a function
value reduction step with a proximal correction step. The former one searches along
an arbitrary descent direction in the Euclidean space instead of a vector in the tangent
space of the Stiefel manifold. Meanwhile, the latter one minimizes a first-order proximal approximation of the objective function in the range space of the current iterate to
make Lagrangian multipliers associated with orthogonality constraints symmetric at
any accumulation point. The global convergence has been established for the proposed
methods. Preliminary numerical experiments demonstrate that the new methods significantly outperform other state-of-the-art first-order approaches in solving various
kinds of testing problems.</p>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.SO-2020-0008},
url = {https://global-sci.com/article/82355/multipliers-correction-methods-for-optimization-problems-over-the-stiefel-manifold}
}