Solving an optimistic MILP-MILP bilevel problem with coin-or/MibS¶
Problem Definition¶
This example is taken from [10] and is a bilevel problem where the upper level is a mixed-integer linear program (MILP) and the lower level is a mixed-integer linear program (MILP).
The problem is formulated as follows:
\[\begin{split}\begin{align}
\min_{x, y} \quad & -x + -10 y \\
\text{s.t.} \quad & x \in \mathbb Z_{\ge 0 },\\
& y\in
\begin{array}[t]{rl}
\displaystyle \underset{y}{\text{arg min}} \quad & y \\
\text{s.t.} \quad & -25 x + 20 y \leq 30, \\
& x + 2 y \leq 10, \\
& 2 x - y \leq 15, \\
& 2 x + 10 y \geq 15, \\
& y \geq 0, \\
& y \in \mathbb Z_{\ge 0}.
\end{array}
\end{align}\end{split}\]