/mialm_code_share

A manifold inexact augmented Lagrangian method for nonsmooth optimization on Riemannian manifold

Primary LanguageMATLABGNU Affero General Public License v3.0AGPL-3.0

Code of paper "A manifold inexact augmented Lagrangian method for nonsmooth optimization on Riemannian manifold"

Our code is based on "manopt toolbox" and code in paper "Proximal Gradient Method for Nonsmooth Optimization over the Stiefel Manifold"

MIALM is a algorithm developed for solving the nonsmooth optimization problems on Riemannian manifold: $$ \min\limits_{X \in \mathcal{M}} f (X) + h(\mathcal{A}(X)) .$$ Here, $f(X): \mathcal{M} \rightarrow \mathbb{R}$ is smoooth, $h(X):\mathbb{R}^m \rightarrow \mathbb{R}$ is convex but nonsmooth, $\mathcal{A}:\mathcal{M} \rightarrow \mathbb{R}^m$ is a linear operator, and the feasible set $\mathcal{M}$ is a Riemannian manifold.

References

If you use these codes in an academic paper, please cite the following papers.

Kangkang, Deng, and Peng Zheng, An inexact augmented Lagrangian method for nonsmooth optimization on Riemannian manifold,IMA Journal of Numerical Analysis).

Authors

To Contact Us

If you have any questions or find any bugs, please feel free to contact us by email (dengkangkang@pku.edu.cn).

License

You can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

MIALM 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. Please see the GNU Lesser General Public License for more details.