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The method used in QCQP



1 comment

  • Jaromił Najman
    Gurobi Staff Gurobi Staff

    The binary product of a binary/integer variable with a binary/integer/continuous variable can be linearized to obtain a MIP formulation, see Multiplication of a continuous and a binary variable. Since Gurobi is able to linearize these products and the remaining quadratic terms in your model are convex, you don't see the message "Continuous model is non-convex -- solving as a MIP". However, once you make your variables continuous, this reformulation is no longer possible, your model becomes non-convex and Gurobi has to now solve an MIQCP instead of a MIP. It is not at all guaranteed that the continuous MIQCP version of your model is any harder or easier than the previous MIP version.

    For non-convex MIQCPs, Gurobi uses a spatial branch-and-bound (B&B) algorithm, which is basically the standard MIP B&B but it also allows to branch on continuous variables occurring in non-convex terms. For more details on global optimization and the spatial B&B algorithm, please refer to, e.g., Horst & Tuy 1996.

    Best regards, 


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