Uniform tree approximation by global optimization techniques

In this paper we present adaptive algorithms for solving the uniform continuous piecewise affine approximation problem (UCPA) in the case of Lipschitz or convex functions. The algorithms are based on the tree approximation (adaptive splitting) procedure. The uniform convergence is achieved by means of global optimization techniques for obtaining tight upper bounds of the local error estimate (splitting criterion). We give numerical results in the case of the function distance to 2D and 3D geometric bodies. The resulting trees can retrieve the values of the target function in a fast way.