Pyomo constraint: use continuous variable as boolean?

Question

I am looking to use a continuous variable in a bool statement. For example, if m.N[t] is the continuous variable, I'd like to do the following:

@m.Constraint(m.t) def success(m,t): if m.N[t] == 0: return m.d[t] = 0

I get the following errors:

ERROR: Rule failed when generating expression for Constraint success with index 0: ValueError: Constraint 'success[0]': rule returned None.

Constraint rules must return either a valid expression, a 2- or 3-member
tuple, or one of Constraint.Skip, Constraint.Feasible, or
Constraint.Infeasible.  The most common cause of this error is forgetting
to include the "return" statement at the end of your rule.

ERROR: Constructing component 'success' from data=None failed: ValueError: Constraint 'success[0]': rule returned None.

Constraint rules must return either a valid expression, a 2- or 3-member
tuple, or one of Constraint.Skip, Constraint.Feasible, or
Constraint.Infeasible.  The most common cause of this error is forgetting
to include the "return" statement at the end of your rule.

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Answer 1

You cannot do this. There is a way to simulate a binary variable by imposing the constraint

x*(1-x) = 0

but that is much worse than just using a binary variable.

To be complete: there is a GDP (Generalized Disjunctive Programming) extension.