[PPL-devel] Proof

[P M Hill]

Hi,

-- 

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.
> 

Where can I find this?

ciao,
 Pat

> 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.
> 
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