I'm new to Gurobi in Python and I am wondering if there is way to express/code "for some" in the following constraint:

$x_i+x_j +x_k+x_l =2$ for some $i, j, k,l \in \{0,1,2,...., 10\}$, where $x_i$ are binary variables.

Question: Is there a way to express the "for some" $i, j,k,$ and $l$ in a certain set ?


1 Answer 1


The existence of some $4$-subset with sum $2$ is equivalent to having at least two $x_i=1$ and at least two $x_i=0$, so impose $2\le \sum_i x_i \le 9$.


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