Indicator Constraint Definition for Bounds

Answered

Phillip Meng

• October 13, 2022 08:42

Hello,

We are trying to implement constraints such that logically:

x = 0 -> f = 0 (this is easy, x binary f continuous).

However, we want to ensure that for our model that:

x = 1 -> f > 0

But this sense can't be encoded. 

Is it true that the first equation forces the second, or should we write the second as:

x = 1 -> f >= 0 and this follows correctly, or do we do an increment such that:

x = 1 -> f >= epsilon

We can also use other constraint else to force this behaviour perhaps - seeking guidance.

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• 

  Jonasz Staszek

  Community Moderator

  • October 13, 2022 08:56

  

  

  

  Hi Phillip,

  you can model this via indicator constraints. Perhaps these two posts (here and here) will be helpful.

  Best regards
  Jonasz

   

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  Jaromił Najman

  Gurobi Staff

  • October 13, 2022 09:26

  Hi Phillip,

  To briefly add on Jonasz' answer:

  Is it true that the first equation forces the second

  No, if you encode x=0 -> f=0, then for x=1, f can by anything, i.e., it can be f=0. If you really want to make sure that f is > 0 then, you have to use an epsilon for x=1 as you proposed. Note that this epsilon should not be smaller than the FeasibilityTol you are using. Something like epsilon = 1e-4 should work fine.

  Best regards, 
  Jaromił

   

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  Phillip Meng

  • October 14, 2022 00:29

  

  

  

  Thank you both, that clarifies our thinking on our modelling implementation.

  :)

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