A matrix-free smoothing algorithm for large-scale support vector machines

Abstract

This paper is concerned with the iterative solution of sequences of Karush-Kuhn-Tucker (KKT) systems arising from smoothing Newton-type algorithms applied to support vector machines (SVMs). Every perturbed Newton step is crucial for the efficiency of the overall algorithm. However, the KKT systems based on smoothing reformulation become increasingly ill-conditioned as the smoothing parameter approaches to zero. By exploiting preconditioning techniques, we propose a matrix-free smoothing algorithm for solving large-scale support vector machines. Numerical results and comparisons are given to demonstrate the effectiveness and speed of the algorithm.