  Due to the non-smoothness of the Hinge loss in SVM, it is difficult to obtain
a faster convergence rate with modern optimization algorithms. In this paper,
we introduce two smooth Hinge losses $\psi_G(\alpha;\sigma)$ and
$\psi_M(\alpha;\sigma)$ which are infinitely differentiable and converge to the
Hinge loss uniformly in $\alpha$ as $\sigma$ tends to $0$. By replacing the
Hinge loss with these two smooth Hinge losses, we obtain two smooth support
vector machines(SSVMs), respectively. Solving the SSVMs with the Trust Region
Newton method (TRON) leads to two quadratically convergent algorithms.
Experiments in text classification tasks show that the proposed SSVMs are
effective in real-world applications. We also introduce a general smooth convex
loss function to unify several commonly-used convex loss functions in machine
learning. The general framework provides smooth approximation functions to
non-smooth convex loss functions, which can be used to obtain smooth models
that can be solved with faster convergent optimization algorithms.
