# How to find the $K$-nearest neighbor vertexs in a polyhedron defined by a set of linear inequalities?

Consider a polyhedron $$\mathcal{P}$$ defined by a set of linear inequalities, i.e.,

$$\mathcal{P} = \left\{ x \in \{0,1\}^N \mid Ax\le b \right\}$$

Suppose $$\mathcal{P}\neq \emptyset$$. If I have a point in $$\mathcal{P}$$, how to find its $$K$$-nearest neighbor vertices in $$\mathcal{P}$$?