Re: [Bug-glpk] bug in simplex for small dimensions ?

[Andrew Makhorin]

>    Thanks for the explanation. If I understand
>   well this is a case where the default scaling
>   (geom mean + equil scaling but skip if LP is well scaled)
>   gives bad results.

Yes. You may look at max|aij| and min|aij| before and after scaling;
these are displayed on the terminal.

>  I was really surprised so I sent this
>   bug report (as geometrically the problem appears
>   very simple, and also  any couple of neighbouring constraints
>   should gives a very well conditionned matrix).

The glpk simplex solver is insufficiently smart to improve the original
lp instance.

> 
>   Btw  when I set the scaling to:
> 
> geometric mean scaling + round scale factors to power of 2
> equilibration scaling
> equilibration scaling + round scale factors to power of 2
> 
>   I get an accurate result.
> 
>   But not with:
> 
>    geom mean + equil scaling + round scale factors to power of 2
> 
> And as you said no scaling is good too here. So for this particular
> constraint matrix, equilibration scaling seems less sensible to this
> problem of a tiny value.
> 

GM scaling works well if the problem is badly scaled, but not in the
case of tiny coefficients.

> PS : The tiny value comes from the fact that the problem was set
> in an automatic way from a numerical code.

This is a frequent error. The program that generates lp data should make
necessary checks and replace tiny coefficients with exact zero.