Uniform tree approximation by global optimization techniques (Q600944)

Let \(f\) be a convex (or a Lipschitz) function of \(d\) variables. The authors present procedures for approximation \(f\) by uniformly continuous, piecewise affine functions, and they present an algorithm for finding tight upper-bounds for the error. The procedure produces approximations that converge uniformly. As examples the authors offer numerical experiments using as the target function, \(f\), the distance from a point to a geometric figure.