properties of Minkowski’s functional
, for all and
where denotes the interior of
where denotes the closure of
where the denotes the boundary of .
Minkowski’s functional is a useful tool to prove propositions and solve exercises. Let us see an example
Example Let be a convex subset of . Show that , where denotes the set of extreme points of .
If then from this follows that and . Now we hypothesize that then there is a real number such that and so . Therefore we have that , that contradicts to the fact that
|Title||properties of Minkowski’s functional|
|Date of creation||2013-03-22 15:45:04|
|Last modified on||2013-03-22 15:45:04|
|Last modified by||georgiosl (7242)|