A Fixed-Point Proximity Approach to Solving the Support Vector Regression with the Group Lasso Regularization

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.