Does Gurobi 9.0 guarantee global optimality for MICQP?
OngoingHi,
I wonder if Gurobi 9.0 guarantees global optimality for MICQP or not.
My problem is MIQCP which includes nonconvex quadratic constraints and binary variables. I set 'NonConvex = 2'.
I found an instance that Gurobi does not provide a global solution. I know a feasible solution for the instance. Gurobi returns a solution which has a worse objective value. Moreover, when I add a few constraints more to guide Gurobi to find the solution I know, it returns better solution.
So, I want to confirm that Gurobi does not guarantee global optimality. Also, if so, I wonder what the meanings of absolute gap and relative gap are because Gurobi's report said there is no gap.
Thanks,
Jongeun

Hi Jongeun,
Gurobi searches for globally optimal solutions to MIQCPs. We'll reach out to you through our online support portal to investigate this.
The absolute gap is the absolute difference between the incumbent objective value and the dual objective bound (i.e., lower bound for minimization problems). The relative gap is this value divided by the incumbent objective value. If the incumbent objective value is zero but the dual objective bound is nonzero, the relative gap is defined to be infinity. If both bounds are zero, the relative gap is defined to be zero.
Thanks,
Eli
0 
This issue was resolved by upgrading from Gurobi 9.0.0 to Gurobi 9.0.2. Gurobi 9.0.0 was the first version to support nonconvex MIQCPs, and this MIQCPrelated bug has since been fixed.
Eli
0 
Using Gurobi 9.0.2 for nonconvex MIQCP, I am still facing an issue where the solution is not global. If I warm start the problem, the solution stays in local optima, while avoiding warm start leads to a global optima.
1 
Hi,
Does this problem still prevail with Gurobi 9.0.3? Is yes, could you provide a LOG file of the problematic run?
Best regards,
Jaromił0
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