The robust Huber M-estimator, a differentiable cost function that is quadra
tic for small errors and linear otherwise, is modeled exactly, in the origi
nal primal space of the problem, by an easily solvable simple convex quadra
tic program for both linear and nonlinear support vector estimators. Previo
us models were significantly more complex or formulated in the dual space a
nd most involved specialized numerical algorithms for solving the robust Hu
ber linear estimator [3], [6], [12], [13], [14], [23], [28]. Numerical test
comparisons with these algorithms indicate the computational effectiveness
of the new quadratic programming model for both linear and nonlinear suppo
rt vector problems. Results are shown on problems with as many as 20,000 da
ta points, with considerably faster running times on larger problems.