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
Famous quotes containing the words proper and/or function:
“Exaggeration is in the course of things. Nature sends no creature, no man into the world, without adding a small excess of his proper quality. Given the planet, it is still necessary to add the impulse; so, to every creature nature added a little violence of direction in its proper path, a shove to put it on its way; in every instance, a slight generosity, a drop too much.”
—Ralph Waldo Emerson (1803–1882)
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