Numerical solution of the Minkowski problem

[摘要] 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. (C) 2001 Elsevier Science B.V. All rights reserved.

[发布日期] 2001-12-15

[关键词] support function;mixed volume;curvature function;spherical harmonics;Newton's method