In
mathematics, the
epigraph or
supergraph of a
function f :
Rn→
R is the
set of points lying on or above its
graph:
The
strict epigraph is the epigraph with the graph itself removed:
The same definitions are valid for a function that takes values in
R ∪ ∞. In this case, the epigraph is empty if and only if
f is identically equal to infinity.