Large quadratic programs in training Gaussian support vector machines

We consider the numerical solution of the large convex quadratic program arising in training the learning machines named support vector machines. Since the matrix of the quadratic form is dense and generally large, solution approaches based on explicit storage of this matrix are not practicable. Well known strategies for this quadratic program are based on decomposition techniques that split the problem into a sequence of smaller quadratic programming subproblems. For the solution of these subproblems we present an iterative projection-type method suited for the structure of the constraints and very effective in case of Gaussian support vector machines. We develop an appropriate decomposition technique designed to exploit the high performance of the proposed inner solver on medium or large subproblems. Numerical experiments on large-scale benchmark problems allow to compare this approach with another widely used decomposition technique. Finally, a parallel extension of the proposed strategy is described.