Originally posted by: J5JK_chao_lei

The introduction of lazy constraint in the user manual states that "Lazy constraints are only (and always) checked when an integer-feasible solution candidate has been identified".

This really confuses me, since I am not sure whether lazy constraints are also checked and satisfied when LP relaxation at a new node is solved such that a tighter bound might be produced. This sounds more reasonable to me rather than that lazy constraints are only checked when an integer-feasible solution candidate has been identified.

Could anyone clarify my confusion? Thanks a lot!
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Originally posted by: SystemAdmin

It appears that lazy constraint callbacks are only called when CPLEX generates a potential new incumbent. I was working with one today and stuck a print statement in it that executed whenever the callback was entered. It was entered only at those nodes where a new incumbent arose.

Paul

Mathematicians are like Frenchmen: whenever you say something to them, they translate it into their own language, and at once it is something entirely different. (Goethe)
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Originally posted by: SystemAdmin

That is correct. Lazy constraint callbacks are only invoked when a new potential incumbent is found. If you want a callback that is invoked at every node then you need to use a UserCutCallback.
ATTENTION: By definition a lazy constraint is allowed to cut off integer feasible solutions while a (user) cut may only cut off fractional solutions.
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Originally posted by: J5JK_chao_lei

Maybe I didn't state my question clear enough. Let me put it in this way: After lazy constraint callbacks is invoked when a new potential incumbent is found and a "lazy" cut is added so that the potential incumbent would be rejected, does this "lazy" cut have any other effects over the model, as like strengthening the best bound or so?
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Originally posted by: SystemAdmin

The separated lazy constraint is added as a row to the model, so that no future incumbent will ever violate it.
In that sense it may improve the dual bound of linear relaxations of the model.
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Originally posted by: J5JK_chao_lei

Thank you very much for your quick response, Daniel.
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