- #1
mertcan
- 345
- 6
- Homework Statement
- Show that there exist an optimal solution which is a convex combination of L+1 extreme points of P
- Relevant Equations
- minkowski or resolution equations(maybe caratheodory theorem)
Hi everyone hope you are well, I would like to express what I have done for this question:
Proving and employing caratheodory theorem we can say that any point in polyhedron can be expressed as a convex combination of at most n+1 points (where n is the space dimension) in same polyhedron that also implies at most n+1 extreme points can be used to define any point as a convex combination. As you see in the question optimal point should be the element of P as well as side constraints but really do not know how can we exactly an optimal solution as a convex combination of L+1 extreme points of P even we have a hint in the question. Could you help me?