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 - <p style="text-align: justify;">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.</p>