Support vector learning with quadratic programming and adaptive step size barrier-projection

Abstract

We consider a support vector machine training problem involving a quadratic objective function with a single linear equality constraint and a box constraint. Using quadratic surjective space transformation to create a barrier for the gradient method, an iterative support vector learning algorithm is derived. We further derive a stable steepest descent method to find the stop-size in order to reduce the number of iterations to reach the optimal solution. This method offers speed improvement over the fixed step-size gradient method, in particular for QP problems with ill-conditioned Hessian.