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I am trying to solve an optimization programming model involving a non-linear constraint with a square root. It follows (in a simplified form): $X_i\ge\sqrt{A_i/B_i}$ where $X_i,A_i,B_i$ are positive variables.

Can you please give me some indications to solve?

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  • $\begingroup$ Hi and welcome to OR.SE. Is there any index associated with A and B? Do you want to linearize the constraint? $\endgroup$ Nov 30 '20 at 17:41
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    $\begingroup$ You tagged the question "mixed-integer-programming". Are any of the variables integer-valued? $\endgroup$
    – prubin
    Nov 30 '20 at 18:56
  • $\begingroup$ @OguzToragay Yes, both variable A and B are associated to index i, as for X. All the variables are integer. $\endgroup$ Nov 30 '20 at 19:38
  • $\begingroup$ Please provide more information on the objective and any other constraints. Viewed in isolation, this constraint could be handled, by squaring both sides, with Geometric Programming, although that is not linearization.Depending on the rest of the model, mnaybe it makes sense to handle it as a nonlinear constraint $X_i^2B_i \ge A_i$? $\endgroup$ Dec 2 '20 at 13:17