In
mathematics, especially
convex analysis, the recession cone of a set is a
cone containing all
vectors such that recedes in that direction. That is, the set extends outward in all the directions given by the recession cone.[1]
Mathematical definition
Given a nonempty set for some
vector space, then the recession cone is given by
In a finite-dimensional space, then it can be shown that if 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.[6]
^Zălinescu, Constantin (1993). "Recession cones and asymptotically compact sets". Journal of Optimization Theory and Applications. 77 (1). Springer Netherlands: 209–220.
doi:
10.1007/bf00940787.
ISSN0022-3239.
S2CID122403313.
In
mathematics, especially
convex analysis, the recession cone of a set is a
cone containing all
vectors such that recedes in that direction. That is, the set extends outward in all the directions given by the recession cone.[1]
Mathematical definition
Given a nonempty set for some
vector space, then the recession cone is given by
In a finite-dimensional space, then it can be shown that if 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.[6]
^Zălinescu, Constantin (1993). "Recession cones and asymptotically compact sets". Journal of Optimization Theory and Applications. 77 (1). Springer Netherlands: 209–220.
doi:
10.1007/bf00940787.
ISSN0022-3239.
S2CID122403313.