Numerical solution of the Minkowski problem

We present a numerical procedure for solving the Minkowski problem, i.e., determining the convex set corresponding to a given curvature function. The method is based on Minkowski's isoperimetric inequality concerning convex and compact sets in R 3 . The support function of the target set is approximated in finite function space, so the problem becomes one of constrained optimization in R n , which in turn is solved by Newtonian (or other) iteration. We prove some properties of the optimization function and the constraining set and present some numerical examples.