When is
$\begin{equation} \min_X \max_Y f(X,Y) \end{equation}$
globally solvable? I.e., when can we find global solution for the optimization problem?
I am not looking for reformulations. Is it only when $f$ is concave in $Y$ and convex in $X$?
When is
$\begin{equation} \min_X \max_Y f(X,Y) \end{equation}$
globally solvable? I.e., when can we find global solution for the optimization problem?
I am not looking for reformulations. Is it only when $f$ is concave in $Y$ and convex in $X$?
There are primarily two things -
A convex domain enables us to make strong comments regarding the global maxima and minima.
The objective function will have a maximum iff it is concave in the domain and min iff it is convex. This statement can be made if we have been given that the domain in convex.