Re: [Help-glpk] fraction with vars

[Michael Hennebry]

On Sat, 28 Apr 2012, Andrew Makhorin wrote:

> > I have a problem with calculating a fraction, the reason is that both
> > the nominator and denominator are variables.
> > So I am looking for some way to make this linear:
> > x_suj = p_s * (y_suj/w_su) or well just find what this fraction
> > is: y_suj/w_su
> > where p_s is a constant, x,y and w are integer variables. and I also
> > need to avoid the division with 0 problem.
> > Anyone know some tips/tricks for this?
>
> Another way is to replace the variables by their logarithms:
>
>   ln x_suj = ln p_s + ln y_suj - ln w_su
>
> and then, depending on the context, model the exponenta
>
>   z = exp(ln z)
>
> by a piecewise linear function using SOS2 constraints; see
> http://lists.gnu.org/archive/html/help-glpk/2007-06/msg00005.html
> http://winglpk.sourceforge.net/media/glpk-sos2_02.pdf

To me, the other suggestions seem better.
They are a bit smaller and still all-integer.
I think that something similar with fewer variables could be done,
but more analysis would be needed.

--
Michael   address@hidden
"On Monday, I'm gonna have to tell my kindergarten class,
whom I teach not to run with scissors,
that my fiance ran me through with a broadsword."  --  Lily