Minimax centre estimation for inspection of spherical parts

Abstract

A mathematical programming formulation is presented for the problem of finding the centre and radius of the sphere such that the largest distance from a sample of points to the boundary of the sphere is minimized. This problem has application in spherical parts inspection. The problem is non-convex, so necessary optimality conditions are developed and used in an exact algorithm. An heuristic technique is shown to produce very good solutions in a short time. Computational experience is included.