Warning of max constraint violation exceeding tolerance in MIQCP

I am using Gurobi version 10.0.1 to solve problems formulated as mixed-integer programs with linear objective function and all linear constraints except for a set of constraints which are quadratic convex.

The quadratic constraints are perspective constraints of the form:
v[i]^2 <= u[i]y[i] for i={1,...,100}
where v,u are non-negative continuous variables, whereas y is a binary variable. They can also be expressed as rotated second-order cones.

I am trying to solve instances of this problem, but on every instance there is a warning in the log file that says (I am copying and pasting one of these warnings) "Warning: max constraint violation (4.8070e-01) exceeds tolerance". I tried setting several parameters to avoid this, without success. I don't know what to do because I can't rely on the optimal solution found if it says it is violating some constraints.

The parameters I tested are: MIPGap = 0.0, FeasibilityTol = 1e-9, IntFeasTol = 1e-9, OptimalityTol = 1e-9, Presolve = 0, MIPGapAbs = 0, PSDTol = 0, BarQCPConvTol = 0, BarConvTol = 0. I also tested PreMIQCPForm = 2 together with BarHomogeneous = 1.

I am solving the problem without any callback, simply using the function model.optimize(). I am not setting other parameters than the ones I listed above. The problem admits solution (e.g., with y=1), so it cannot be infeasible, nor unbounded. I can send some instances/logs if it can help understanding what is going on (in case, please let me know how). I'd be grateful if you could provide some guidance.

David Torres Sanchez

Gurobi Staff

July 31, 2023 11:13 Edited

You can try different PreMIQCPForm = 0, or 1 or PreQLinearize = 0, 1, 2.

Also if you have any warnings in the log you may want to try the NumericFocus = 1, 2, or 3 or Quad = 1.

You may also want to reduce the bounds for the variables if possible.

Cheers,
David

Warning of max constraint violation exceeding tolerance in MIQCP

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