A FIXED-POINT PROXIMITY APPROACH TO SOLVING THE SUPPORT VECTOR REGRESSION WITH THE GROUP LASSO REGULARIZATION

作者：Li, Zheng; Song, Guohui; Xu, Yuesheng^*

来源：International Journal of Numerical Analysis and Modeling, 2018, 15(1-2): 154-169.

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

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.

• 出版日期2018
• 单位中山大学