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.
