Multipliers Correction Methods for Optimization Problems over the Stiefel Manifold

• DOI: 10.4208/csiam-am.so-2020-0008
• Publication Date: 2021-08-31T07:59:02Z
• Authors: Lei Wang Lei Wang; Bin Gao Bin Gao; Xin Liu Xin Liu
• Keywords: Stiefel manifold; Manifold (fluid mechanics)

We propose a class of multipliers correction methods to minimize differentiable function over the Stiefel manifold. The proposed combine value reduction step with proximal step. former one searches along an arbitrary descent direction in Euclidean space instead vector tangent Meanwhile, latter minimizes first-order approximation objective range current iterate make Lagrangian associated orthogonality constraints symmetric at any accumulation point. global convergence has been established for methods. Preliminary numerical experiments demonstrate that new significantly outperform other state-of-the-art approaches solving various kinds testing problems.