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Let $c \in \mathbb R^n$, $A \in \mathbb R^{m \times n}$, $b \in \mathbb R^m$, and $I \subseteq \{1,2,\ldots,n\}$. Consider the Mixed integer linear program (MILP) $$ \begin{split} f^* = &\max \; ...

My question is motivated by the fact, that among other ways, it is possible to restrict a variable to two discrete values, e.g. the prototypical $0$ and $1$, via an optimization constraint: $$\max(\...