sci.op-research

On Mar 26, 7:27=A0am, A.L. wrote:
> On Wed, 26 Mar 2008 03:52:01 GMT, Paul Rubin wrote:
> >Peter wrote:
> >>>> Peter
> >>> The objective function is the same in both problems? =A0Are the variab=
les
> >>> the same in both problems (which would not make much sense)? =A0I can =
only
> >>> make sense of this if the variables in the outer problem parameterize
> >>> the constraints of the inner problem, but that would mean the inner
> >>> problem has different decision variables and likely a different
> >>> objective. =A0Perhaps you could supply a small scale specific example.=

>
> >>> /Paul- Hide quoted text -
>
> >>> - Show quoted text -
>
> >> A sample problem can be as following:
>
> >> (P)
> >> Min z1=3Dx
> >> X <=3D y
>
> >> (P')
> >> Min z2=3D0
> >> y <=3D b =A0(b is a constant)
> >> z1_min <=3D k =A0(k is a constant)
>
> >> where z1_min, is the optimal value of the objective function for the
> >> problem (P). The decision variables in the problem (P') parameterize
> >> the constraints in the problem (P).
>
> >Neglecting for the moment the fact that, as written, (P) is unbounded, I
> >think I see (in general terms) where you are headed. =A0I believe the
>
> ... and you claim that you understand what is, quote, "Min z2=3D0"?...
>
> A.L.- Hide quoted text -
>
> - Show quoted text -

Actually, at that time I just wanted to write an outer problem, say
(P'), in such a way that the decision variables in problem (P')
parameterize
the constraints in problem (P). By Min z2=3D0 I was trying to say that
the problem (P') does not have a specific objective function.

Peter