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Volume 15, Issue 1-2
A Fixed-Point Proximity Approach to Solving the Support Vector Regression with the Group Lasso Regularization

Zheng Li, Guohui Song & Yuesheng Xu

Int. J. Numer. Anal. Mod., 15 (2018), pp. 154-169.

Published online: 2018-01

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  • Abstract

We introduce an optimization model of the support vector regression with the group lasso regularization and develop a class of efficient two-step fixed-point proximity algorithms to solve it numerically. To overcome the difficulty brought by the non-differentiability of the group lasso regularization term and the loss function in the proposed model, we characterize its solutions as fixed-points of a nonlinear map defined in terms of the proximity operators of the functions appearing in the objective function of the model. We then propose a class of two-step fixed-point algorithms to solve numerically the optimization problem based on the fixed-point equation. We establish convergence results of the proposed algorithms. Numerical experiments with both synthetic data and real-world benchmark data are presented to demonstrate the advantages of the proposed model and algorithms.

  • Keywords

Two-step fixed-point algorithm, proximity operator, group lasso, support vector machine, ADMM.

  • AMS Subject Headings

65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

li_zheng 2011@163.com (Zheng Li)

gsong@clarkson.edu (Guohui Song)

yxu06@syr.edu (Yuesheng Xu)

  • BibTex
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  • TXT
@Article{IJNAM-15-154, author = {Li , ZhengSong , Guohui and Xu , Yuesheng}, title = {A Fixed-Point Proximity Approach to Solving the Support Vector Regression with the Group Lasso Regularization}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {15}, number = {1-2}, pages = {154--169}, abstract = {

We introduce an optimization model of the support vector regression with the group lasso regularization and develop a class of efficient two-step fixed-point proximity algorithms to solve it numerically. To overcome the difficulty brought by the non-differentiability of the group lasso regularization term and the loss function in the proposed model, we characterize its solutions as fixed-points of a nonlinear map defined in terms of the proximity operators of the functions appearing in the objective function of the model. We then propose a class of two-step fixed-point algorithms to solve numerically the optimization problem based on the fixed-point equation. We establish convergence results of the proposed algorithms. Numerical experiments with both synthetic data and real-world benchmark data are presented to demonstrate the advantages of the proposed model and algorithms.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10561.html} }
TY - JOUR T1 - A Fixed-Point Proximity Approach to Solving the Support Vector Regression with the Group Lasso Regularization AU - Li , Zheng AU - Song , Guohui AU - Xu , Yuesheng JO - International Journal of Numerical Analysis and Modeling VL - 1-2 SP - 154 EP - 169 PY - 2018 DA - 2018/01 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10561.html KW - Two-step fixed-point algorithm, proximity operator, group lasso, support vector machine, ADMM. AB -

We introduce an optimization model of the support vector regression with the group lasso regularization and develop a class of efficient two-step fixed-point proximity algorithms to solve it numerically. To overcome the difficulty brought by the non-differentiability of the group lasso regularization term and the loss function in the proposed model, we characterize its solutions as fixed-points of a nonlinear map defined in terms of the proximity operators of the functions appearing in the objective function of the model. We then propose a class of two-step fixed-point algorithms to solve numerically the optimization problem based on the fixed-point equation. We establish convergence results of the proposed algorithms. Numerical experiments with both synthetic data and real-world benchmark data are presented to demonstrate the advantages of the proposed model and algorithms.

Li , ZhengSong , Guohui and Xu , Yuesheng. (2018). A Fixed-Point Proximity Approach to Solving the Support Vector Regression with the Group Lasso Regularization. International Journal of Numerical Analysis and Modeling. 15 (1-2). 154-169. doi:
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