I have the following problem: \begin{align} \max_{x} \quad & \| x - \hat{x} \|_2^2 \\ \text{s.t.} \quad & x^\top a_i \leq b_i, \quad \forall i \in \{ 1,\ldots,N \}, \end{align} where $x \in \mathbb{R}^n$ is the decision variable and $\hat{x}, a_1, \ldots, a_N, b_1, \ldots, b_N$ are given.
I would like to prove this problem is NP-hard. I have read that maximizing a quadratic form over a polytope is NP-hard, but I have not found a formal proof of this statement. Apparently, one can prove it using some kind of reduction argument to an 0-1 integer program, or to the $k$-clique problem, but I was not able to apply these arguments to my problem.
So my question is: how do I prove that my problem is NP-hard?