In mathematical analysis (in particular convex analysis) and optimization, a proper convex function is a convex function f taking values in the extended real number line such that
for at least one x and
for every x. That is, a convex function is proper if its effective domain is nonempty and it never attains . Convex functions that are not proper are called improper convex functions.
A proper concave function is any function g such that is a proper convex function.
Read more about Proper Convex Function: Properties
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