Q:

Smallest sphere intersecting lines in R^3

I have N lines in R^3 (that are very likely skew). I'm looking for an efficient method of computing the radius (and position) of the smallest sphere that intersects every line.
I suspect that there's a solution related to the 'smallest sphere enclosing points' problem, but I failed to find it.
(The purpose is to be able to do bundle adjustment without needing to make the inferred point positions visible to the optimizer).

A:

The distance from a point to a line is a convex function, and the maximum of convex functions in convex, so locating a point that minimizes the maximum of its distances to the lines is a convex problem, therefore it should be relatively easy to solve using modern software for convex optimization.

