It's matlab, I'd need C++. I guess it might be easy enough to convert though. It doesn't change the nature of my question anyway, which is how it works.

@LiviuNicolaescu I had a thought about this problem I don't think apart from compactness I cannot assume more.

@LiviuNicolaescu I'll make my question as more specific as possible then.

And again, given my assumption (i.e. $f : \mathcal{M} \to \mathbb{R}$) in your list you can pick the scalar curvature. I think I've given already a stricter assumption already, i.e. regular submanifolds in $\mathbb{R}^n$, or isn't this enough?

@LiviuNicolaescu As an example I'm trying to optimize curvature, I have this manifold and I want to find the point whose curvature is maximum (or a local optimizer).