  This paper deals with an extension of the Support Vector Machine (SVM) for
classification problems where, in addition to maximize the margin, i.e., the
width of strip defined by the two supporting hyperplanes, the minimum of the
ordered weighted sum of the deviations of miclassified individuals is
considered. Since the ordered weighted sum includes as particular case the sum
of these deviations, the classical SVM model is a particular case of the model
under study. A quadratic continuous formulation for the case in which weights
are sorted in non-decreasing order is introduced, and a mixed integer quadratic
formulation for general weights is presented. In both cases, we show that these
formulations allow us the use of kernel functions to construct non linear
classifiers. Besides, we report some computational results about the predictive
performance of the introduced approach (also in its kernel version) in
comparison with other SVM models existing in the literature.

Optimization and Control