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International audienceWe 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 Hölder 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 functions is shown to be almost surely converging to zero, and the rate of convergence is proved to be optimal

L 1-optimal linear programming estimator for periodic frontier functions with Hölder continuous derivative