Crossposted at Computational Science SE
Consider a quadratic programming problem with the following format: $$ \text{min} Q(x) = c^Tx+\frac{1}{2}x^TDx \\ $$ $$ \text{s.t.} Ax\leq b, \\ x\geq 0 $$ where $D$ is a $n\times n$ positive definite matrix and $A$ is a $m\times n$ matrix. We know when $n$ and $m$ are small, for example, when both of them are 2, we can solve the problem and get the exact solution using the KKT condition. However, when $n$ and $m$ are large (meaning that we have a large-scale quadratic programming problem. I think we are also able to get the exact solution using the KKT condition.
However, to the best of my knowledge, I cannot find any reference for this. The book 'quadratic programming' said that this type of question can be solved in polynomial time (page 3), for example, the interior point method. But as far as I know, the interior point method only can get the near-optimal solution making the objective function within the acceptable tolerance (like $10^{-7}$). We can also refer to this post about using the interior point method to solve the quadratic programming method.
My question: is it possible for us to get the exact solution to the aforementioned question when $n$ and $m$ are large? How expensive it is if we want to get the exact solution (global optimum) of the quadratic programming problem I mentioned before? And how it relates to the number of $m$? Is it impossible to calculate it even with computers? I will really appreciate it if you can offer some references for this problem.
