Sampling arbitrary point from system of linear inequalities - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T11:25:01Z http://mathoverflow.net/feeds/question/46117 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/46117/sampling-arbitrary-point-from-system-of-linear-inequalities Sampling arbitrary point from system of linear inequalities Eunsoo Oh 2010-11-15T15:08:30Z 2010-11-15T15:55:10Z <p>How to choose an arbitrary point from a polytope defined by system of linear inequalities, Ax &lt; b ? (Here A is an m-by-n matrix, x is n-by-1 and b is m-by-1.) I just want to find one ARBITRARY point that satisfies Ax &lt; b and NOT satisfies Ax = b.</p> http://mathoverflow.net/questions/46117/sampling-arbitrary-point-from-system-of-linear-inequalities/46121#46121 Answer by Gilead for Sampling arbitrary point from system of linear inequalities Gilead 2010-11-15T15:55:10Z 2010-11-15T15:55:10Z <p>I agree with Boris -- you want to solve an LP. If you would like to solve it numerically, just pose it like this: <code>\begin{align} &amp; \min 0 \\ s.t. \quad &amp; Ax + e\leq b \end{align}</code> where $e \in \mathbb{R}^m$ is a vector containing $\epsilon$'s, which is some numerical tolerance.</p>