Closed convex function
Terms in Maths / From Wikipedia, the free encyclopedia
In mathematics, a function is said to be closed if for each
, the sublevel set
is a closed set.
Equivalently, if the epigraph defined by
is closed, then the function
is closed.
This definition is valid for any function, but most used for convex functions. A proper convex function is closed if and only if it is lower semi-continuous.[1]