Linearized Alternating Direction Method of Multipliers for Constrained Nonconvex Regularized Optimization

Linbo Qiao, Bofeng Zhang, Jinshu Su, Xicheng Lu
Proceedings of The 8th Asian Conference on Machine Learning, PMLR 63:97-109, 2016.

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 this Paper

BibTeX
@InProceedings{pmlr-v63-qiao37, 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}, pages = {97--109}, year = {2016}, editor = {Durrant, Robert J. and Kim, Kee-Eung}, volume = {63}, series = {Proceedings of Machine Learning Research}, address = {The University of Waikato, Hamilton, New Zealand}, month = {16--18 Nov}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v63/qiao37.pdf}, url = {https://proceedings.mlr.press/v63/qiao37.html}, 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.} }
Endnote
%0 Conference Paper %T Linearized Alternating Direction Method of Multipliers for Constrained Nonconvex Regularized Optimization %A Linbo Qiao %A Bofeng Zhang %A Jinshu Su %A Xicheng Lu %B Proceedings of The 8th Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Robert J. Durrant %E Kee-Eung Kim %F pmlr-v63-qiao37 %I PMLR %P 97--109 %U https://proceedings.mlr.press/v63/qiao37.html %V 63 %X 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.
RIS
TY - CPAPER TI - Linearized Alternating Direction Method of Multipliers for Constrained Nonconvex Regularized Optimization AU - Linbo Qiao AU - Bofeng Zhang AU - Jinshu Su AU - Xicheng Lu BT - Proceedings of The 8th Asian Conference on Machine Learning DA - 2016/11/20 ED - Robert J. Durrant ED - Kee-Eung Kim ID - pmlr-v63-qiao37 PB - PMLR DP - Proceedings of Machine Learning Research VL - 63 SP - 97 EP - 109 L1 - http://proceedings.mlr.press/v63/qiao37.pdf UR - https://proceedings.mlr.press/v63/qiao37.html AB - 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. ER -
APA
Qiao, L., Zhang, B., Su, J. & Lu, X.. (2016). Linearized Alternating Direction Method of Multipliers for Constrained Nonconvex Regularized Optimization. Proceedings of The 8th Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 63:97-109 Available from https://proceedings.mlr.press/v63/qiao37.html.

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