Given this optimization problem,
$Max \quad Q(x)$
$s.t., \quad x \in X$
$\quad \sum_{i=1}^{n} x_i^2 = k$
where $x_i$ are integers, $x \in X$ is a set of linear inequalities, k is a parameter, and Q(x) is a quadratic function of x.
I'm interested in knowing if there is an efficient way to solve this problem. Given the fact that the second constraint is in the form of equality, the problem is not convex or conic.