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

[Gabor Retvari]

Dear GLPK users,

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.

Thanks,
Gabor

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