# Quadratic optimization in Gurobi with constraint

I have a question of understanding in Gurobi: I have an objective function in which my optimization variable x is squared. I have solved this bsiher by a quadratic objective function with $$x$$, $$x$$. Now, however, I need another optimization variable in this equation, so according to other posts here, I have set up a constraint that returns me the optimization variable $$z = x^2$$ and use this instead of $$x, x$$ in my objective function. Correspondingly, I also set the parameter for NonConvex to 2. What irritates me now is that I get different values for my objective function when using $$x, x$$ or $$z$$. Maybe someone can explain to me why this is the case or maybe I am doing something wrong.

• Do you mean you get different solution or different optimal objective value? If same objective value, then the problem has a non-unique minimizer, and there is no reason to expect that two completely different formulations of the problem would yield the same solution (in particular when you create one version using a simple QP, and the other approach with a nonconvex model which requires a completely different and much more computationally demanding solution machinery) – Johan Löfberg Apr 19 at 7:57
• The values of the objective function also deviate, but only very slightly. This is then probably also related to the calculation method and the computational effort, or? – Handballer73 Apr 20 at 6:54
• The optimality tolerances are probably a couple of orders of magnitude larger in the nonconvex solver than the convex solver, so it depends on what you mean with slightly – Johan Löfberg Apr 20 at 7:06
• I just did an evaluation and the deviations are negligible. Thank you for the tip and the hint, I simply had a thinking error. – Handballer73 Apr 20 at 7:20