  Support vector machine is an important and fundamental technique in machine
learning. In this paper, we apply a semismooth Newton method to solve two
typical SVM models: the L2-loss SVC model and the \epsilon-L2-loss SVR model.
The semismooth Newton method is widely used in optimization community. A common
belief on the semismooth Newton method is its fast convergence rate as well as
high computational complexity. Our contribution in this paper is that by
exploring the sparse structure of the models, we significantly reduce the
computational complexity, meanwhile keeping the quadratic convergence rate.
Extensive numerical experiments demonstrate the outstanding performance of the
semismooth Newton method, especially for problems with huge size of sample data
(for news20.binary problem with 19996 features and 1355191 samples, it only
takes three seconds). In particular, for the \epsilon-L2-loss SVR model, the
semismooth Newton method significantly outperforms the leading solvers
including DCD and TRON.
