Variable Projection Methods for Large Quadratic Programs in Training Support Vector Machines

In this paper we analyse the variable projection methods for the solution of the convex quadratic programming problem arising in training the learning techinque named Support Vector Machine. Since the Hessian matrix of the objective function is large and dense the problem is faced by decomposition techniques that require to solve a sequence of quadratic programming subproblems of smaller size. For the solution of these subproblems, we consider variable projection methods based on different steplength updating rules. In particular, we introduce a new steplength selection that implies remarkable convegence rate improvements. The effectiveness of the variable projection method combined with this steplength selection is evaluated in comparison with standard routines on well known benchmark problems.