Indicator Constraint Definition for Bounds
AnsweredHello,
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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Community Moderator
Hi Phillip,
you can model this via indicator constraints. Perhaps these two posts (here and here) will be helpful.
Best regards
Jonasz1 -
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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,
Jaromił1 -
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Thank you both, that clarifies our thinking on our modelling implementation.
:)
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