Quadratic objective function auxiliary terms result in nonconvex model?

Awaiting user input

Vineet Jagadeesan Nair

January 25, 2023 02:57

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I'm formulating a convex optimization problem with quadratic (convex) objective function and linear constraints. I needed to introduce auxiliary variables for each of the quadratic objective terms, and corresponding quadratic equality constraints to define them. However, gurobi now recognizes the model as nonconvex and requires me to set the NonConvex parameter to 2 to solve the model - even though the original problem is convex. How can I avoid this issue?

Related to

• Nonconvex
• QP

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  Jaromił Najman

  • Gurobi Staff

  January 25, 2023 10:09

  Hi Vineet,

  Nonlinear equality constraints are always nonconvex. Thus, Gurobi requires you to set the NonConvex parameter to 2.

  I needed to introduce auxiliary variables for each of the quadratic objective terms, and corresponding quadratic equality constraints to define them.

  Why exactly do you need auxiliary variables and constraints when your original model is quadratic? If there is no option of avoiding the auxiliaries, you might think whether using \(\leq\) inequalities instead of equality constraints is valid for your case. This might make your model convex again if each inequality is convex.

  Best regards, 
  Jaromił

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