  We propose new estimates for the frontier of a set of points. They are
defined as kernel estimates covering all the points and whose associated
support is of smallest surface. The estimates are written as linear combinatio-
ns of kernel functions applied to the points of the sample. The coefficients of
the linear combination are then computed by solving a linear programming
problem. In the general case, the solution of the optimizat- ion problem is
sparse, that is, only a few coefficients are non zero. The corresponding points
play the role of support vectors in the statistical learning theory. The L_1
error between the estimated and the true frontiers is shown to be almost surely
converging to zero, and the rate of convergence is provided. The behaviour of
the estimates on finite sample situations is illustrated on some simulations.
