Add Conditional Constraint

回答済み

Ruoyun Chen

2021年02月17日 19:09

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Hi,

I'm having constraints that should be activated once the solution of one variable is greater than a certain number. 

For example: I have two variables x and y. 

What I want to implement is: 

if x>5: then f(x)>g(y). where f() and g() are certain expression of x and y. 

if x<=5, then this constraint will not be activated. 

How should I implement that?

Really appreciate!

 

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• 正式なコメント

  

  Simranjit Kaur

  • Gurobi Staff

  2025年06月23日 02:59 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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  Ruoyun Chen

  2021年02月17日 19:24

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  The reason I'm asking this is because every time I try to implement x>5 it reports:

  '>' not supported between instances of 'Var' and 'float'

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  Jaromił Najman

  • Gurobi Staff

  2021年02月18日 14:25 編集済み

  Hi,

  Strict inequalities are not allowed in state-of-the-art optimization software due to compactness of the feasible set. The best thing you could model is an approximation of your statement which would be
  
  if \(x\geq 5+\epsilon_1\) then \(f(x)\geq g(x) + \epsilon_2\)

  for some small positive \(\epsilon_1,\epsilon_2\).

  You can achieve this by first modeling the relationship

  if \(x\geq 5+\epsilon_1 \Leftrightarrow \delta=1\)

  as described in this stackexchange post. This would be

  \[\begin{align}
  \epsilon_1&=10^{-6}\\
  x &\geq 5+\epsilon_1 - 10\cdot(1-\delta)\\
  x &\leq 5+\epsilon_1 + 10\cdot \delta\\
  \delta &\in \{0,1\}
  \end{align}\]
  You can then use an indicator constraint to model the relationship

  if \(\delta=1\) then \(g(y)+\epsilon_2-f(x) \leq 0\)

  Best regards,
  Jaromił

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  Ruoyun Chen

  2021年02月18日 14:38

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  Thanks a lot for your quick response Jaromił!

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