Linearized Alternating Direction Method of Multipliers for Constrained Nonconvex Regularized Optimization
Abstract
In this paper, we consider a class of constrained nonconvex regularized minimization problems, where the constraints is linearly constrained. It was reported in the literature that nonconvex regularization usually yields a solution with more desirable sparse structural properties beyond convex ones. However, it is not easy to obtain the proximal mapping associated with nonconvex regularization, due to the imposed linearly constraints. In this paper, the optimization problem with linear constraints is solved by the Linearized Alternating Direction Method of Multipliers (LADMM). Moreover, we present a detailed convergence analysis of the LADMM algorithm for solving nonconvex compositely regularized optimization with a large class of nonconvex penalties. Experimental results on several real-world datasets validate the efficacy of the proposed algorithm.
Cite
Text
Qiao et al. "Linearized Alternating Direction Method of Multipliers for Constrained Nonconvex Regularized Optimization." Proceedings of The 8th Asian Conference on Machine Learning, 2016.Markdown
[Qiao et al. "Linearized Alternating Direction Method of Multipliers for Constrained Nonconvex Regularized Optimization." Proceedings of The 8th Asian Conference on Machine Learning, 2016.](https://mlanthology.org/acml/2016/qiao2016acml-linearized/)BibTeX
@inproceedings{qiao2016acml-linearized,
title = {{Linearized Alternating Direction Method of Multipliers for Constrained Nonconvex Regularized Optimization}},
author = {Qiao, Linbo and Zhang, Bofeng and Su, Jinshu and Lu, Xicheng},
booktitle = {Proceedings of The 8th Asian Conference on Machine Learning},
year = {2016},
pages = {97-109},
volume = {63},
url = {https://mlanthology.org/acml/2016/qiao2016acml-linearized/}
}