# How to linearize a max min objective function?

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?