Question about model.AddGenConstrIndicator()
AnsweredI was debating someone about the behavior of Gurobi. We have a model using indicator constraints.
Let's say you create
int target1_value = 1;
for (int col = 0; col < sims.cols; ++col)
{
gap_value[col] = model.AddVar(0, GRB.INFINITY, 0, GRB.CONTINUOUS, "gaps");
GRBVar gap = model.AddVar(-GRB.INFINITY, GRB.INFINITY, 0, GRB.CONTINUOUS, "gap");
b[col] = model.AddVar(0, 1, 0, GRB.BINARY, "b");
And then use
model.AddGenConstrIndicator(b[col], 1, gap == gap_value[col] - target1_value, "penalty_amt");
model.AddGenConstrIndicator(b[col], 0, gap == 0, "no_penalty_amt");
}
From my understanding of the documentation the model will seek to optimize the best values of b[col]. The debate was over whether or not b[col] is set to be 1 when the gap is positive or 0 otherwise.
Therefore, I understand that the gap being positive or not has nothing to do with the value of b[col], the model will choose this based on the constraints. What is debated is whether the value will be set based on the linear expression in the function argument.
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What is debated is whether the value will be set based on the linear expression in the function argument.
I am not sure what you mean by the function argument.
If I understand you correctly, your assessment is true. As you mentioned, the values of variables \(b\) enforce restrictions on the values of variables \(\mbox{gap}\). For example, it is still possible for the \(b\) variable to be 1 and the \(\mbox{gap}\) variable to be 0 where \(\mbox{gap_value}\) equals \(\mbox{target1_value}\).
Best regards,
Maliheh
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Hi Maliheh, what I meant by function argument was the linear expression argument in AddGenConstrIndicator, whether the gap is positive or not. The debate was whether gap being positive enforced b == 1. But my view was the other way around, as I believe the documentation supports. b== 1 enforces the linear constraint. This also appears to be what you previous comment says as well.
The intended purpose of the constraints was to impose the constraint with a positive gap, and not impose them with a negative or 0 gap. But as implemented I do not believe they are doing this.
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What you have implemented is if \(b = 1\), then \(\mbox{gap} = \mbox{gap_value} - \mbox{target1_value}\).
Given the lower bound of 0 for the variable \(\mbox{gap_value}\), the variable \(\mbox{gap}\) is enforced to be between \(-\mbox{target1_value}\) and \(\infty\). If the \(\mbox{target1_value}\) is a positive constant, it means that the \(\mbox{gap}\) variable is not forced to be strictly positive. You would need additional constraints to enforce if \(b = 1\), then \(\mbox{gap} \geq \epsilon\) with \(\epsilon\) being the smallest positive meaningful value for the \(\mbox{gap}\) variable.
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