Closed convex function
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. For a convex function which is not proper there is disagreement as to the definition of the closure of the function.Properties
