Optimization of the Hausdorff distance between convex polyhedrons in R3

Abstract

In this article, approximation of sets is under consideration using convex polyhedrons in the three dimensional Euclidean space. In the problem statement, it is necessary to find such disposition of two given polyhedrons A and B that the Hausdorff distance between them obtains the minimal value. Elements of convex analysis, non-smooth analysis, and numerical geometry are used for construction numerical algorithms solving this problem. Numerical algorithms are implemented in the software whose efficiency is demonstrated in applications. © 2015, IFAC Hosting by Elsevier Ltd.