Let us suppose that I have a $\max \min$ objective function that only depends on one set of variables:

$\underset{x}\max \underset{y}\min dy$

Associated with the linear set of constraints and right size real matrices and vectors $A, B, b$ and $d$:

$Ax + By\le b$

$(n,m)\in \mathbb N^2$.

$x\in \{0,1\}^n$

$y\in \{0,1\}^m$

Meaning that the model tries to chose the values of $x$ so that $\underset{y}\min dy$ is maximized.

Is it possible to linearize this objective function to get an ILP or a MILP at the end?


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