QCP Results Change for Different Versions of Gurobi

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  • Jaromił Najman

    The difference between the Gurobi versions is not a bug in this case. The issue boils down to the convergence criterion of interior point algorithms. The main issue with the model you provided is reaching primal feasibility for both Gurobi versions. The theory on interior-point methods only talks about relative violations, so we can't expect to always hit absolute numbers for feasibility tolerances. And Second Order Cones make that even harder. This explains the difference in objective value when setting the NumericFocus parameter, because the absolute primal feasibility is actually not fulfilled without setting the parameter. So in both versions, the final solution point is slightly infeasible making a comparison between solution values rather impracticable.

    As an alternative to the NumericFocus setting, you might want to use the BarHomogeneous algorithm which is numerically more stable but a bit slower than the standard Barrier algorithm. Often using the homogeneous algorithm should still be faster than using the NumericFocus parameter.

    Another alternative might be to try a different formulation of the problem where the quadratic constraint is less dense while still maintaining convexity.

    If you are interested in more details on interior-point algorithms, we recommend having a look at the book by Stephen J. Wright on Primal-Dual Interior-Point Methods.

    Best regards,
    Jaromił

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