Minimum volume sphere bounding all points as a linear programming problem

Question

I want to find the smallest sphere which encapsulate a set of points $x_i \in \mathbb{R}^d$.

I can formulate is as

$$ \arg \min_{a \in \mathbb{R}^d, r} r \quad\quad \text{s.t.} \quad || x_i - a|| \leq r $$

Can it be formulated as a linear programming problem?
If not, is there a reasonable approximation?

https://math.stackexchange.com/questions/1639716/how-can-l-1-norm-minimization-with-linear-equality-constraints-basis-pu?rq=1 — Sutanu Majumdar, Dec 09 '23 at 16:59
@SutanuMajumdar, I think the link is about a different norm. — Mark, Dec 09 '23 at 23:23

score 1 · Answer 1 · answered Dec 10 '23 at 16:27

1

You can solve the problem directly via second-order cone programming.

answered Dec 10 '23 at 16:27

RobPratt

Nice. Are there resources which explains in layman words the described work there? – Mark Dec 10 '23 at 19:49

1 Answers1