Sorry if the question is trivial. I have the following optimization problem which I think is not convex because of the binary constraints. But I do not know what is this problem then. Here is the optimization problem.
$$ \text{minimize } ||Ax - b||_2 \\ s.t. \sum\limits_{i=1}^{n} x_i = \ell,\\ x \in \lbrace 0,1\rbrace $$
In fact, the goal is to only select $\ell$ points from $A$, such that the sum of those selected points is close to $b$.
It's a mixed-integer second order cone optimization problem. MOSEK is arguably the best solver for this problem. If $\ell$ is small, you could brute-force the solution.