I am using Gurobi and Quadprog in Matlab. I want to verify that both optimization software give me the same result. Quadprog is using the interior-point-convex and Gurobi the barrier method. I think these methods are the same, because the names are just synonyms of each other. Correct me if I am wrong, please. However, Gurobi is using other default values for the tolerance and constraint parameters then Quadprog. I found that the default value of the OptimalityTolerance is different, but I don't know which parameters I should check further and which are important. Furthermore, Quadprog is using a StepTolerance (Termination tolerance on
x; a positive scalar.), but I don't know which parameter this fits from Gurobi. I have already found a list of which parameters Gurobi is using, but I am not really into it even if I read the descriptions of the parameters.
Furthermore, I am solving a MPC (Model Predictive control) QP problem with different formulations (sparse and dense) using Gurobi. The sparse formulation is gives lower computations times (using tic toc) at larger horizons then the dense formulation. This is the other way around when I am using Quadprog. Does anyone have an idea why this is the case? Could Gurobi handle sparse matrice structures much more easier then Quadprog? How could I verify that the results are good?
I would be really thankfull if someone could answer these questions. If you have any sources about this, I would also be very happy. Thanks in advance.
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