Exterior-Point Method for Support Vector Machines

We present an exterior-point method (EPM) for training dual-soft margin support vector machines (SVMs). The EPM stems from nonlinear rescaling and augmented Lagrangian methods and allows iterates to approach the solution of a constrained nonlinear optimization problem from the exterior of the feasible set. Furthermore, the EPM produces and solves a well-conditioned system of linear equations at each iteration; thus, avoiding numerical inaccuracies that can occur when solving ill-conditioned systems. Therefore, the EPM may be an attractive alternative to existing quadratic programming solvers for training SVMs. We report numerical results for training the SVM with the EPM on data up to several thousand data points from the UC Irvine Machine Learning Repository.