  Support vector machines (SVMs) are successful modeling and prediction tools
with a variety of applications. Previous work has demonstrated the superiority
of the SVMs in dealing with the high dimensional, low sample size problems.
However, the numerical difficulties of the SVMs will become severe with the
increase of the sample size. Although there exist many solvers for the SVMs,
only few of them are designed by exploiting the special structures of the SVMs.
In this paper, we propose a highly efficient sparse semismooth Newton based
augmented Lagrangian method for solving a large-scale convex quadratic
programming problem with a linear equality constraint and a simple box
constraint, which is generated from the dual problems of the SVMs. By
leveraging the primal-dual error bound result, the fast local convergence rate
of the augmented Lagrangian method can be guaranteed. Furthermore, by
exploiting the second-order sparsity of the problem when using the semismooth
Newton method,the algorithm can efficiently solve the aforementioned difficult
problems. Finally, numerical comparisons demonstrate that the proposed
algorithm outperforms the current state-of-the-art solvers for the large-scale
SVMs.
