POLYMATROID

In mathematics, the 'polymatroid' defined by a given matroid $(E,r)$ is the set of all functions
:$w:E\; omathbb\{R\}$
such that
:$w(e)ge\; 0$
for all $ein\; E$
:$sum\_\{ein\; S\}w(e)le\; r(S)$
for all
:$Ssubset\; E;$.
Polymatroids are related to the convex polytopes seen in linear programming, and have similar uses.
The notion was introduced by Jack Edmonds in 1970.