A Matlab solver for Riemannian optimization on the symplectic Stiefel manifold
This solver is to solve the following optimization problem,
- min f(X), s.t. X' J2n X = J2p
where X is a 2n-by-2p matrix, J2n = [0 In; -In 0], and In is the n-by-n identity matrix.
- the nearest symplectic matrix problem:
min ||X-A||^2_F, s.t. X' J2n X = J2p.
- the extrinsic mean problem:
min 1/N \sum_{i=1}^{i=N}||X-A_i||^2_F, s.t. X' J2n X = J2p.
- minimization of the Brockett cost function:
min trace(X'AXN-2BX'), s.t. X' J2n X = J2p.
- symplectic eigenvalue computation of spd or spsd:
min trace(X'AX), s.t. X' J2n X = J2p.
- symplectic model order reduction:
min ||M-XX^\dag M||, s.t. X' J2n X = J2p, where X^\dag = J2p' X' J2n
- Riemannian optimization on the symplectic Stiefel manifold, SIAM Journal on Optimization, 31-2 (2021), 1546-1575.
- Geometry of the symplectic Stiefel manifold endowed with the Euclidean metric, Geometric Science of Information: 5th International Conference, GSI 2021, Lecture Notes in Computer Science, 12829 (2021), 789–796.
- Computing symplectic eigenpairs of symmetric positive-definite matrices via trace minimization and Riemannian optimization, SIAM Journal on Matrix Analysis and Applications, 42-4 (2021), 1732–1757.
- Optimization on the symplectic Stiefel manifold: SR decomposition-based retraction and applications, arXiv:2211.09481, (2022).
- P.-A. Absil (UCLouvain, Belgium)
- Bin Gao (UCLouvain, Belgium)
- Nguyen Thanh Son (Thai Nguyen University of Sciences, Vietnam)
- Tatjana Stykel (University of Augsburg, Germany)
Copyright (C) 2020, P.-A. Absil, Bin Gao, Nguyen Thanh Son, Tatjana Stykel
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/