Hi Pat, can you help me to find a formal proof (or an example it is not true) to the following assertion?
EXTREMAL RAYS ARE STABLE WHEN COMBINED WITH ANY VECTOR OF THE LINEALITY SPACE.
I found it in H. Leverge - A note on Chernikova's Algorithm - Publication Interne 635 - February 1992 - page 9.
I guess "stable" means that the combination between an extremal ray with an element of the lin. space is an extremal ray.
I think it is intuitive that it's true, but I can't find a formal proof!
Also, I found (in Leverge page 4) this result:
if the set G = cone{y} + lin.space (C) is a face of C, then y is called an extremal ray of C and G a minimal proper face of C;
where, given a set X cone{X} is the set of all positive combination of all vectors in X.
Can this help to demonstrate the assertion above?
Thanks, Angela.