Quadratic programming

Question

For a research project I am interested in minimizing $x^TQx$ under the constraints $Qx \le b$, where $Q$ is a positive definite matrix and $b$ is a vector of negative elements. I have solved this with the Gurobi Solver, but as the matrix $Q$ is not sparse, there are lots of terms in the objective. I was wondering if one can take advantage of the constraints being so closely related to the objective.