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I am implementing a NLP problem in pyomo, and I am getting some issues for this constraint:

\begin{equation} \forall i \in \lbrace 1, N \rbrace , \forall j \in \left\{1, M \right\}: Y_{i,j} \cdot S_{i,j} = \max_{k} \big(p_{i,k} \cdot S_{i,k} \big) \end{equation}

where:

$Y_{i,j}$ is a binary decision variable equal to 1 if element j is a match to i, 0 otherwise.

$S_{i,j}$ is a continous decision variable such as $0 \leq S_{i,j} \leq 1$.

$p_{i,j}$ is a binary parameter equal to 1 if j is a candidate of i, 0 otherwise.

Basically, this constraint is to select j for i such as $S_{i,j}$ is the maximum value. Eventually, I have another constraint to ensure the unicity of the selected match:

\begin{equation} \forall i \in \lbrace 1, N \rbrace : \sum_{j=1}^M Y_{i,j} = 1 \end{equation}

Now to implement the former constraint in pyomo, I have tried this code:

    def pred_selection_rule(model, i, j):
        return (model.Yij[i,j] * model.Sij[i,j] == max(model.pij[i,k] * model.Sij[i,k] for k in model.M))
    model.pred_selection = Constraint(model.N, model.M, rule=pred_selection_rule)

Then I got this error:

ERROR: Rule failed when generating expression for constraint pred_selection
    with index (1, 1): TypeError: Cannot create a compound inequality with
    identical upper and lower
        bounds using strict inequalities: constraint infeasible: 0.0  <
        Sij[1,40] and Sij[1,40] < 0.0
ERROR: Constructing component 'pred_selection' from data=None failed:
        TypeError: Cannot create a compound inequality with identical upper
        and lower
        bounds using strict inequalities: constraint infeasible: 0.0  <
        Sij[1,40] and Sij[1,40] < 0.0

I have also tried to replace the constraint coding (i.e. second line) by:

        return  inequality(0.0, (model.pij[i,k] * model.Sij[i,k] for k in model.M), model.Yij[i,j] * model.Sij[i,j])

This is even worse as the problem cannot be instantiated.

any suggestion on how to fix it?

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Maybe you can replace your equality constraint with two inequality $\leq$ and $\ge$ constraints. Also, have a look at this link

| improve this answer | |
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  • $\begingroup$ Thanks for the answer, but it didn't work. I had a look on the link, but it does not provide what I am looking for. I ended up linearizing the constraint, which made the problem even larger. $\endgroup$ – Betty Jun 5 at 13:42

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