Linear Least Squares Fit of Sphere to Points

Question

I\'m looking for an algorithm to find the best fit between a cloud of points and a sphere.

That is, I want to minimise

where C is the centre

Answer 1

There are no matrix equations forthcoming. Your choice of E is badly behaved; its partial derivatives are not even continuous, let alone linear. Even with a different objective, this optimization problem seems fundamentally non-convex; with one point P and a nonzero radius r, the set of optimal solutions is the sphere about P.

You should probably reask on an exchange with more optimization knowledge.