  This paper considers various models of support vector machines with ramp
loss, these being an efficient and robust tool in supervised classification for
the detection of outliers. The exact solution approaches for the resulting
optimization problem are of high demand for large datasets. Hence, the goal of
this paper is to develop algorithms that provide efficient methodologies to
exactly solve these optimization problems. These approaches are based on three
strategies for obtaining tightened values of the big M parameters included in
the formulation of the problem. Two of them require solving a sequence of
continuous problems, while the third uses the Lagrangian relaxation to tighten
the bounds. The proposed resolution methods are valid for the l1-norm and
l2-norm ramp loss formulations. They were tested and compared with existing
solution methods in simulated and real-life datasets, showing the efficiency of
the developed methodology.
