Recession cone

In mathematics, especially convex analysis, the recession cone of a set

That is, the set extends outward in all the directions given by the recession cone.

is additionally a convex set then the recession cone can equivalently be defined by If

is a nonempty closed convex set then the recession cone can equivalently be defined as The asymptotic cone for

is defined by By the definition it can easily be shown that

is nonempty, closed and convex.

[5] In infinite-dimensional spaces, then the relation between asymptotic cones and recession cones is more complicated, with properties for their equivalence summarized in.