Orthant (source code)
= Orthant
{title2=$\{x\in\mathbb R^n:\sigma_i x_i\geq0\text{ for all }i\},\quad\sigma_i\in\{-1,1\}$}
{wiki}
A closed coordinate-sign region of <Euclidean space>. The $2^n$ orthants cover the space. An orthant contains no nontrivial affine line: for a nonzero direction, some coordinate eventually violates its sign restriction in one direction. Adding orthant inequalities to a nonempty <linear polyhedron> therefore permits construction of a <basic feasible solution> even when the original polyhedron has no vertex.
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