Two smooth support vector machines for $$\varepsilon $$-insensitive regression

In this paper, we propose two new smooth support vector machines for \(\varepsilon \)-insensitive regression. According to these two smooth support vector machines, we construct two systems of smooth equations based on two novel families of smoothing functions, from which we seek the solution to \(\varepsilon \)-support vector regression (\(\varepsilon \)-SVR). More specifically, using the proposed smoothing functions, we employ the smoothing Newton method to solve the systems of smooth equations. The algorithm is shown to be globally and quadratically convergent without any additional conditions. Numerical comparisons among different values of parameter are also reported.