# mialm_code

**Repository Path**: DENGKANGKANG/mialm_code

## Basic Information

- **Project Name**: mialm_code
- **Description**: code of "An inexact augmented Lagrangian method for nonsmooth optimization on Riemannian manifold"
- **Primary Language**: Matlab
- **License**: AGPL-3.0
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 2
- **Forks**: 0
- **Created**: 2021-11-30
- **Last Updated**: 2023-12-09

## Categories & Tags

**Categories**: Uncategorized

**Tags**: optimization, manifold

## README

 # Code of paper "[A manifold inexact augmented Lagrangian method for nonsmooth optimization on Riemannian manifold](https://arxiv.org/pdf/1911.09900)"

Our code is based on "[manopt toolbox](https://www.manopt.org/index.html)" and code in paper "[Proximal Gradient Method for Nonsmooth Optimization over the Stiefel Manifold](https://epubs.siam.org/doi/abs/10.1137/18M122457X)" 



MIALM is a algorithm developed for solving the nonsmooth optimization problems on Riemannian manifold.

$$
\begin{equation*}
  \begin{aligned}
    \min\limits_{X \in \mathcal{M}} \hspace{2mm} & f (X) + h(\mathcal{A}(X)) 
  \end{aligned}
\end{equation*}
$$

Here, $f(X): \mathcal{M} \to \mathbb{R}$ is smoooth, $h(X):\mathbb{R}^m \to \mathbb{R}$ is  convex but nonsmooth, $\mathcal{A}:\mathcal{M}\to \mathbb{R}^m$ 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*](https://arxiv.org/abs/1911.09900), arXiv preprint arXiv:1911.09900 (2019).

## Authors

- [Kangkang Deng](https://kangkang-deng.github.io/) (dengkangkang@pku.edu.cn)
- Zheng Peng (pzheng@fzu.edu.cn)



## 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](https://www.gnu.org/licenses/lgpl-3.0.en.html) 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](https://www.gnu.org/licenses/lgpl-3.0.en.html) for more details.