How to choose an arbitrary point from a polytope defined by system of linear inequalities, Ax < b ? (Here A is an mbyn matrix, x is nby1 and b is mby1.) I just want to find one ARBITRARY point that satisfies Ax < b and NOT satisfies Ax = b.
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I agree with Boris  you want to solve an LP. If you would like to solve it numerically, just pose it like this: $$ \begin{align} & \min 0 \\ s.t. \quad & Ax + e\leq b \end{align} $$ where $e \in \mathbb{R}^m$ is a vector containing $\epsilon$'s, which is some numerical tolerance. 

