“Exposed point”的意思、由来-开放百科全书

词条

Exposed point

释义

In mathematics, an exposed point of a convex set is a point at which some continuous linear functional attains its strict maximum over . Such a functional is then said to expose . Note that there can be many exposing functionals for . The set of exposed points of is usually denoted .

A stronger notion is that of strongly exposed point of which is an exposed point such that some exposing functional of attains its strong maximum over at , i.e. for each sequence we have the following implication: . The set of all strongly exposed points of is usually denoted .

There are two weaker notions, that of extreme point and that of support point of .

3 : Mathematical analysis|Convex geometry|Functional analysis

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