Assume I have $n$ random variables $x$ which need to obey a set of inequality constraints that are linear and can be written as $Ax \leq 0$. Is there a method to sample effectively from these for large $n$, say $n > 10^3$? The first few that are sampled are e.g. from a uniform or exponential distribution, but those constrain the next ones chosen.
Maybe Markov Chain Monte Carlo is what I'm looking for, but the implementations I found require an additional linear equality constraints which I don't want to introduce.
