An inexact smoothing-type algorithm for support vector machines

The smoothing-type algorithm has been successfully applied to solve various optimization problems. In this paper, we propose an inexact smoothing-type algorithm for solving the generalized support vector machines based on a new class of smoothing functions. In general, the smoothing-type method is designed based on some monotone line search and solving a linear system of equations exactly at each iteration. However, for the large-scale problems, solving the linear system of equations exactly can be very expensive. In order to overcome these drawbacks, solving the linear system of equations inexactly and the non-monotone line search technique are used in our smoothing-type method. We show that the proposed algorithm is globally and locally superlinearly convergent under suitable assumptions. Preliminary numerical results are also reported.