  We propose a new estimator based on a linear programming method for smooth
frontiers of sample points. The derivative of the frontier function is supposed
to be Holder continuous.The estimator is defined as a linear combination of
kernel functions being sufficiently regular, covering all the points and whose
associated support is of smallest surface. The coefficients of the linear
combination are computed by solving a linear programming problem. The L1- error
between the estimated and the true frontier functionsis shown to be almost
surely converging to zero, and the rate of convergence is proved to be optimal.
