I have a polyhedron $P$ described by $$ P = \{ x | Ax \preceq b\}, $$ $x \in \mathbf{R}^{n}.$ I want to randomly generate points that are inside $P$.
One way is to just generate random points and select those that satisfy the inequality but obviously this will take quite a long time especially when $P$ has small volume.
Is there any way I can efficiently sample a point that is inside $P$ ?