Sampling arbitrary point from system of linear inequalities - MathOverflow most recent 30 from http://mathoverflow.net2013-05-21T11:25:01Zhttp://mathoverflow.net/feeds/question/46117http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/46117/sampling-arbitrary-point-from-system-of-linear-inequalitiesSampling arbitrary point from system of linear inequalitiesEunsoo Oh2010-11-15T15:08:30Z2010-11-15T15:55:10Z
<p>How to choose an arbitrary point from a polytope defined by system of linear inequalities, Ax < 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 < b and NOT satisfies Ax = b.</p>
http://mathoverflow.net/questions/46117/sampling-arbitrary-point-from-system-of-linear-inequalities/46121#46121Answer by Gilead for Sampling arbitrary point from system of linear inequalitiesGilead2010-11-15T15:55:10Z2010-11-15T15:55:10Z<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>$$
\begin{align}
& \min 0 \\
s.t. \quad & Ax + e\leq b
\end{align}
$$</code>
where $e \in \mathbb{R}^m$ is a vector containing $\epsilon$'s, which is some numerical tolerance.</p>