Second level maximization constraint
AnsweredDear all, I'm trying to run an IGDT algorithm with the following structure;
i.e. I have a maximization term in the objective and a second maximization term in the constraints. Would the multi objective functionality of Gurobi work for this or could this perhaps be solved via some other route I'm currently not seeing?
Thanks in advance!
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Gurobi Staff
Hi Gijs,
Is the problem invalid if you simply remove the maximization term in the constraints?
i.e.
Max f(x) <= y
is true if and only if
f(x) <= y for all x
- Riley
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Hi Riley, the problem is no longer equal when I remove the maximization term in the constraints. This happens since the maximization term is supposed to represent a worst-case outcome which cannot exceed the value delta-r. Whereas when I remove the maximization term the constraint will always be non-binding as their exist many cases for which that objective value will be lower than delta-r.
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Hi Gijs,
Ah I understand now. This is an example of bi-level programming and the multi-objective functionality isn't enough to solve this. In rare cases, you can translate a bilevel program into a single-level program and then solve this with Gurobi (multiple objectives not needed), but in general bilevel programming is not yet supported by Gurobi.
For an overview of the technique to translate special cases of bilevel problems as single level models (and other solution techniques) please see this paper by Kleinert et al.
- Riley
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Thank you Riley, I will take a look that paper!
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