LibADMM Toolbox

1. Introduction

This toolbox solves many sparse, low-rank matrix and low-rank tensor optimization problems by using M-ADMM developed in our paper [1].

2. List of Problems

The table below gives the list of problems solved in our toolbox. See more details in the manual at https://canyilu.github.io/publications/2016-software-LibADMM.pdf.

3. Citation

In citing this toolbox in your papers, please use the following references:

C. Lu, J. Feng, S. Yan, Z. Lin. A Unified Alternating Direction Method of Multipliers by Majorization 
Minimization. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 40, pp. 527-541, 2018
C. Lu. A Library of ADMM for Sparse and Low-rank Optimization. National University of Singapore, June 2016.
https://github.com/canyilu/LibADMM.

The corresponding BiBTeX citation are given below:

@manual{lu2016libadmm,
author       = {Lu, Canyi},
title        = {A Library of {ADMM} for Sparse and Low-rank Optimization},
organization = {National University of Singapore},
month        = {June},
year         = {2016},
note         = {\url{https://github.com/canyilu/LibADMM}}
}
@article{lu2018unified,
author       = {Lu, Canyi and Feng, Jiashi and Yan, Shuicheng and Lin, Zhouchen},
title        = {A Unified Alternating Direction Method of Multipliers by Majorization Minimization},
journal      = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
publisher    = {IEEE},
year         = {2018},
volume       = {40},
number       = {3},
pages        = {527—-541},
}

4. Version History

• Version 1.0 was released on June, 2016.
• Version 1.1 was released on June, 2018. Some key differences are below:
  • Add a new model about low-rank tensor recovery from Gaussian measurements based on tensor nuclear norm and the corresponding function lrtr_Gaussian_tnn.m
  • Update several functions to improve the efficiency, including prox_tnn.m, tprod.m, tran.m, tubalrank.m, and nmodeproduct.m
  • Update the three example functions: example_sparse_models.m, example_low_rank_matrix_models.m, and example_low_rank_tensor_models.m
  • Remove the test on image data and some unnecessary functions

References

[1]	C. Lu, J. Feng, S. Yan, Z. Lin. A Unified Alternating Direction Method of Multipliers by Majorization Minimization. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 40, pp. 527-541, 2018
[2]	C. Lu. A Library of ADMM for Sparse and Low-rank Optimization. National University of Singapore, June 2016. https://github.com/canyilu/LibADMM.