Year: 2021
Author: Lei Wang, Bin Gao, Xin Liu
CSIAM Transactions on Applied Mathematics, Vol. 2 (2021), Iss. 3 : pp. 508–531
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.SO-2020-0008
CSIAM Transactions on Applied Mathematics, Vol. 2 (2021), Iss. 3 : pp. 508–531
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Multipliers correction proximal approximation orthogonality constraint Stiefel manifold.