implement conditional constraint

回答済み

David Mejía

2020年07月15日 19:21

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Hi, 

I´ve been trying to implement this constraint:

if a >=1 then b=1 else b =0

a is a continuous variable 

b is a binary variable

I´ve seen people using the big M to express this, but I can´t get to work properly.

 

Thanks

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  Simranjit Kaur

  • Gurobi Staff

  2025年06月23日 03:09 編集済み

  This post is more than three years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum. Or why not try our AI Gurobot?.
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  Eli Towle

  • Gurobi Staff

  2020年07月15日 21:11

  Hi David,

  This sounds pretty similar to another forum post. There's example code in that thread for implementing a similar logical constraint in Python using indicator constraints.

  Assuming \( a \) is bounded, we can model this on our own. Let \( a \in [\ell, u] \). Given a sufficiently small \( \epsilon > 0 \), we can (approximately) model \( a \geq 1 \iff b = 1\) with the following constraints:

  $$\begin{align*}a &\leq 1 - \epsilon + (u - 1 + \epsilon)b \\ a &\geq b + \ell(1 - b).\end{align*}$$

  • If \( b = 0 \), the first constraint gives us \( a \leq 1 - \epsilon \). The second constraint collapses to \(a \geq \ell\) and thus does not affect the model.
  • If \( b = 1 \), the first constraint becomes \( a \leq u \), which does not affect the model. The second constraint becomes \( a \geq 1 \).

  Does this answer your question?

  Thanks,

  Eli

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  David Mejía

  2020年07月16日 06:41

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  Hi Eli,

  Thank you so much for your help, that answered my question!

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