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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 $X$?

1 Answers 1

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There are primarily two things -

  1. convexity/concavity of domain
  2. convexity/concavity of objective function

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.

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    I did not receive any response after setting the bounty, so I think no one gets bounty from my side.2012-12-07