Proper convex function

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 $-\infty$ . Convex functions that are not proper are called improper convex functions.

单词	Proper concave function
释义	Proper concave function 英语百科 Proper convex function 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 $-\infty$ . Convex functions that are not proper are called improper convex functions.
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Proper concave function

Proper convex function