I am interested in the solutions of a very large quadratic programming (QP) problem\begin{align}\min_{x \in \mathbb{R}^n} & x^T Q x\\\mathrm{subject\ to} & A x = b\\& x \in \{0,1\}^n\end{align}where $n=10^7$, $Q$ is a dense, positive-semidefinite matrix whose entries are natural numbers that can be computed rapidly, and $A \in \mathbb{N}^{n \times 20}$.What is a suitable algorithm for such a large problem, and what is a good implementation?
What is a suitable algorithm for solving a large mixed-integer quadratic program?
optimization;quadratic programming;mixed integer programming