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Non-Convex Quadratic Optimization. Ratio constraints



1 comment

  • Eli Towle
    Gurobi Staff Gurobi Staff

    In (2), the \( p_1 y_i \) and \( p_2 t_i \) terms are all bilinear. You could reduce the number of bilinear terms by creating auxiliary variables for each summation:

    $$\begin{align*} \sum_i a_i x_i &= u_1 \\ \sum_ i b_i y_i &= u_2 \\ \sum_i c_i z_i &= u_3 \\ \sum_i d_i t_i &= u_4 \\ u_1 u_4 &= u_2 u_3. \end{align*}$$

    This formulation is probably worth a try. Be sure to apply the tightest possible bounds on all variables participating in bilinear terms.


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