Augmented Lagrangian Methods for Optimization on Sp(2p,2n)

版本 1.0.0 (13.3 KB) 作者: Harry
Three augmented Lagrangian algorithms for solving optimization problems on the symplectic Stiefel manifold.
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Augmented Lagrangian Methods for Optimization on the Symplectic Stiefel Manifold
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1. Problem and solvers
This package contains Matlab codes for solving the following problem
min_{X\in R^{2n\times 2p}} F(X) s.t X'*J_{2n}*X = J_{2p};
where F:R^{2n\times 2p} \to R is a smooth function. The above problema is solved with three augmented lagrangian algoritmos introduced in the preprint [REF]"Augmented Lagrangian Methods for Optimization on the Symplectic Stiefel Manifold", by Oviedo H. and Lara H., (2025).
Solvers: fun.m Grad_cayley.m, Grad_qr.m, Pen_Approach.m, PenGrad_cayley.m, PenGrad_qr.m, RADMM.m
fun.m --- corresponds to an implementation of the objective function and its gradient.
SGM.m --- corresponds to an implementation of the spectral gradient method to
solve every subproblem (to minimize the augmented Lagrangian function).
ALM.m --- corresponds to an implementation of the ALM algorithm presented in
the reference mentioned above [REF].
ALM2.m --- corresponds to an implementation of the ALM2 algorithm presented in
the reference mentioned above [REF].
ALM3.m --- corresponds to an implementation of the ALM3 algorithm presented in
the reference mentioned above [REF].
spopt.m --- corresponds to the algorithms introduced in: Gao B., Son N. T., Absil P. A.
and Stykel T. (2021). Riemannian optimization on the symplectic Stiefel
manifold. SIAM Journal on Optimization, 31(2): 1546–1575. These
methods are available in https://github.com/opt-gaobin/spopt. This code is
not a proprietary implementation, it will be only used for comparison
purposes.
demo.m --- A Matlab script where a trace minimization problem is randomly
generated and solved with all solvers.
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2. Reference
Harry Oviedo and Hugo Larta. "Augmented Lagrangian Methods for Optimization on the Symplectic Stiefel Manifold". Technical report, 2025;
Harry Oviedo <harry.oviedo@uai.cl>
Hugo Lara <hugo.lara.urdaneta@ufsc.br>
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3. The Authors
We hope that the package is useful for your application. If you have any bug reports or comments, please feel free to email me:
Harry Oviedo, harry.oviedo@uai.cl
Enjoy it!
Harry Oviedo and Hugo Lara.
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Copyright (C) 2025, Harry Oviedo and Hugo Lara.
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.

引用格式

Harry (2026). Augmented Lagrangian Methods for Optimization on Sp(2p,2n) (https://ww2.mathworks.cn/matlabcentral/fileexchange/181008-augmented-lagrangian-methods-for-optimization-on-sp-2p-2n), MATLAB Central File Exchange. 检索时间: .

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