Quadratic programming (polynomial objective and linear constraints) worst-case time complexity

I have a quadratic programming problem (polynomial objective and linear constraints).

I solve it with GUROBI. I wonder what's the worst time complexity of the parallel barrier algorithm. I could not find any reference on google scholar on this method. I know another widely used interior point method, the primal-dual interior point method has a time complexity of \(O(\sqrt{n} \ln(1/\epsilon))\), where n is the number of inequality constraints. Does the parallel barrier algorithm have the same time complexity? If so, could you please recommend a reference for the parallel barrier algorithm?

If not, could please should the time complexity of the algorithm, and also recommend some references?

Thank you so much for your time.

Quadratic programming (polynomial objective and linear constraints) worst-case time complexity

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