1 comment

• Gurobi Staff

Hi Xiaoyu,

No, Gurobi does not directly support solving an optimization problem with an objective function in the form $$\frac{x^\prime Q x}{x^\prime P x}$$. Please check the article on What types of model can Gurobi solve? for the list of models that Gurobi solves.

You can consider defining an auxiliary variable $$y$$ and solve the following optimization problem (assuming minimization):

\begin{align} \min~~ y & \notag \\ \mathrm{st:}~~ & x^\prime Q x - y (x^\prime P x) \leq 0 \notag \end{align}

This is a nonconvex problem and the term $$y (x^\prime P x)$$ includes multilinear terms that you need to model using a series of bilinear constraints. You can check the article on How do I model multilinear terms in Gurobi?

Best regards,

Maliheh