Assume I have a matrix $Q \in \mathbb{R}^{n \times n}$ which is positiv definite and symmetric, and I want to minimize $$ \frac{1}{2} x^T Q x + x^T f $$ on a non-empty convex set $x\in D=\{ v \in \mathbb{R}^n \mid Av\leq 0,\, Bv = c\} $. Such a problem is know as a convex minimisation problem with a unique solution. In matlab I can use the default interior-point-convex method which returns pretty fast a solution.
My question is: What can one say about the complexity to compute the unique solution? Something like how much memory is need and the average amount of computations.
If you care about the computational complexity of QP, not the absolute runtime for a specific instance of the problem, you might want to take a look at the ellipsoid algorithm.