A smoothing approximation for L∞ SVM

Abstract

In this paper, the infinite norm SVM is considered and a novel smoothing approximation function for Support Vector Machine is proposed in attempt to overcome some drawbacks of the former method which are complex, subtle, and sometimes difficult to implement. Firstly, we use Karush-Kuhn-Tucker complementary condition in optimization theory, and the unconstrained non-differentiable optimization model is built. Then the smooth approximation algorithm based on differentiable function is given. Finally, the paper trains the data sets with standard unconstraint optimization method. This algorithm is fast and insensitive to initial point. Theory analysis and numerical results illustrate that the smoothing approximation for the infinite SVM is feasible and effective.