Re: [Help-glpk] minimising after maximising

[Michael Hennebry]

On Mon, 6 Jun 2011, Nick Farrell wrote:

> Wouldn't that mean that z[] was always >= 3?

Yes.  That is what you asked for.

> I want z[j] to be x[j] if x[j] < 3, 3 otherwise.

Minimizing a minimum is trickier.

z[j] <= x[j]
z[j] <= 3
z[j] >= 3 - M[j] b[j]
z[j] >= x[j] - N[j] (1-b[j])

where the b's are new binary variables and the
M's and N's are new, possibly large, constants.

Selecting their values is left as an exercise for the reader.

> On Mon, Jun 6, 2011 at 11:24 AM, Michael Hennebry <
> address@hidden> wrote:
>
> > On Sun, 5 Jun 2011, Nick Farrell wrote:
> >
> >  I'm pretty new to linear programming and would like a quick tip.
> > > In the script below, what I *want* to happen is that I first choose the
> > > worst (ie: max) of x[p] and 3, and then solve for the minimum sum of these
> > > values.
> >
> > z[j]>=x[j]
> > z[j]>=3
> >
> >
> >
> >  ie: I would like z to look like: {1, 2, 3, 3, 3} and then to minimise on
> > > the
> > > sum of these.
> >
> > min SUM z[j]
> >     j

--
Michael   address@hidden
"Pessimist: The glass is half empty.
Optimist:   The glass is half full.
Engineer:   The glass is twice as big as it needs to be."