  We propose new optimal estimators for the Lipschitz frontier of a set of
points. They are defined as kernel estimators being sufficiently regular,
covering all the points and whose associated support is of smallest surface.
The estimators are written as linear combinations of kernel functions applied
to the points of the sample. The coefficients of the linear combination are
then computed by solving related linear programming problem. The L_1 error
between the estimated and the true frontier function with a known Lipschitz
constant is shown to be almost surely converging to zero, and the rate of
convergence is proved to be optimal.
