We propose new methods for estimating the frontier of a set of points. The estimates are defined as kernelfunctions covering all the points and whose associated support is of smallest surface. They are written aslinear combinations of kernel functions applied to the points of the sample. The weights of the linearcombination are then computed by solving a linear programming problem. In the general case, the solutionof the optimization problem is sparse, that is, only a few coefficients are non-zero. The correspondingpoints play the role of support vectors in the statistical learning theory. In the case of uniform bivariatedensities, the L1 error between the estimated and the true frontiers is shown to be almost surely convergingto zero, and the rate of convergence is provided. The behaviour of the estimates on one finite sample situation is illustrated on simulations.