Related: mathoverflow.net/q/376145/134538 Is the answer $\sim \zeta_nV(f^2)$ or $\sim \zeta_n^m V(f^2)$. I am not sure about the exponent of $\zeta_n$. Is the dimension has any role?

Sorry to bother you again, most of the MILP softwares ask only one inequality (one matroix inequality, one matrix equality and one bound inequality. How can I feed this problem into these software, as I here have multiple inequlities and they are not in format of the one required for these software. Any furthur processing needs to be done. It would be great if you could share some info on this. Thanks.

Should we minimize the tolerance $\epsilon$?

One last question, I understood the constraints, but what is it that should be minimized? As I read any MILP problem has constraints and a minimization problem.

Thanks RobPratt. Any algorithm available to solve this?

@Dirk : I thought Lipschitz domain means bounded already, but learnt just now that it isn't. So to add, $\Omega$ is a bounded domain with a smooth boundary.

My question could be really simple or silly, just that I don't know the answer. I am sure I am asking what I intended.

Is it just $h(n) = O(1/n)$?