Suppose there is a set of n linear constraints $\{{a}_{i}^{T}x+{b}_{i}\le 0{\}}_{i=1}^{n}$ with ${a}_{i}\in {\mathbb{R}}^{d}$, ${b}_{i}\in \mathbb{R}$, $x\in {\mathbb{R}}^{d}$. How can I find ${x}^{\ast}$ that maximizes $|\{i\in [n]\mid {a}_{i}^{T}{x}^{\ast}+{b}_{i}\le 0\}|$? Is this problem solvable or can be approximated within polynomial time?

Some reference materials would also be nice. Thanks!

Some reference materials would also be nice. Thanks!