Hi Angela, -- On Thu, 7 Jun 2001, Angela Stazzone wrote:
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!
It can't be true. Have a look at the definition of extreme ray. It is extreme if it is NOT the positive combination of two other rays. Note that a line is just two rays in opposite directions. I would be interested to know what Leverge means by "stable". I've been trying to guess, but without any success. ciao, Pat