max of a convex function

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This may be an obvious question for some: suppose $f$ is a convex function. I would like to solve the problem

$$\max f(x) \\ \text{s.t. }x \in \Omega$$

where $\Omega$ is a regular (say, satisfying MFCQ) convex set. Can anyone suggest a way to do it?

I know how to solve the min problem using KKT condition. But I am unclear about the max case because the negative of $f$ is no longer a convex function. Thanks for any help!