Add Conditional Constraint
AnsweredHi,
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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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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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 relationshipif \(\delta=1\) then \(g(y)+\epsilon_2-f(x) \leq 0\)
Best regards,
Jaromił0 -
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Thanks a lot for your quick response Jaromił!
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