C1,1 approximations of generalized support vector machines

Smoothing methods, extensively used for solving mathematical programming problems and applications, are applied in this paper to approximate some optimization problems arising in the theory of generalized support vector machines. A nonlinear model, which generalizes some previous works, is considered in order to minimize the weighted combination of the error distance and the number of features utilized by the support vector machines. In particular, our smooth approach concerns the use of the class of C1,1 functions to approximate the above nonlinear objects.