Smooth Newton method for implicit Lagrangian twin support vector regression

A new smoothing approach for the implicit Lagrangian twin support vector regression is proposed in this paper. Our formulation leads to solving a pair of unconstrained quadratic programming problems of smaller size than in the classical support vector regression and their solutions are obtained using Newton-Armijo algorithm. This approach has the advantage that a system of linear equations is solved in each iteration of the algorithm. Numerical experiments on several synthetic and real-world datasets are performed and, their results and training time are compared with both the support vector regression and twin support vector regression to verify the effectiveness of the proposed method.