A Semismooth Newton based Augmented Lagrangian Method for Nonsmooth Optimization on Matrix Manifolds

Yuhao Zhou, Chenglong Bao, Chao Ding, Jun Zhu. Preprint. Arxiv:2103.02855.

Usage

Before running our code, please load the package manopt first in MATLAB:

run manopt/importmanopt.m

Then, you can run RunCM.m, RunSPCA.m or RunOrtho.m.

Important note: this is a research software. It is not intended nor designed to be a general purpose software at the moment.

Files

Our codes are in the directory almssn. They depend on two manifold optimization libraries [1, 2]:

• The directory manopt contains the package http://www.manopt.org [1].
• The directory OptM contains Wen's first-order method in Stiefel manifolds; see https://github.com/optsuite/OptM [2]. The file OptStiefelGBB.m was slightly modified to record the intermediate results.

References

• [1]: N. Boumal, B. Mishra, P.-A. Absil, and R. Sepulchre, Manopt, a Matlab toolbox for optimization on manifolds, Journal of Machine Learning Research, 15 (2014), pp. 1455–1459.
• [2]: Z. Wen and W. Yin, A feasible method for optimization with orthogonality constraints, Mathematical Programming, 142 (2013), pp. 397–434.