Is there a way to check if the point is outside of a polytope if polytope is defined as $\mathcal{P}=\{x|a_j^\top x\leq b_j, \;j=1,\dots,m\}$?
I was able to derive the following:
\begin{equation} \min_{j\leq m}\Bigg\{\frac{b_j-a_j^\top x}{\|a_j\|}\Bigg\}. \end{equation}
If the above expression is $\leq 0$, then the point is outside of the polytope. However, the expression above is nonconvex, which is my main concern.