Re: [Help-glpk] LP Modeling question: avoiding 'x' to be a scalar multiple of 'y'

[Michael Hennebry]

On Wed, 7 Nov 2007, Gabor Retvari wrote:

> I would like to ask your help regarding a strange linear feasiility problem I
> have: I am serching for some [x,y] vector in a (polyhedral) set 'P', so
> that 'x' is not a scalar multiple of 'y'. That is, I want to find
>
> [x,y] \in P = {[x,y]: Ax + By \le b, x \ge 0, y \ge 0}
>
> such that there is no scalar k > 0, for which k * x = y !
>
> Can someone enlighten me how I could impose this restriction on 'x' and 'y' by
> an appropriate objective function or additional constraints (or both)? I am
> mostly interested in linear solutions (so that what I get is an LP), but
> basically any nonlinear programming formulation will do as well.

The bad news is that you can't.
The good news is that you don't need to.
With floating point, it's rather unlikely that a
multidimensional y would be a scalar multiple of x.

-- 
Mike   address@hidden
"Horse guts never lie."  -- Cherek Bear-Shoulders