As we said before, a typical recommendation for improving numerics is to limit the
range of constraint matrix coefficients. The rationale behind
this guideline is that terms to be added in a linear expression should
be of comparable magnitudes so that rounding errors are minimized.
For example:
is usually considered a potential source of numerical instabilities
due to the wide range of the coefficients in the constraint.
However, it is easy to implement a simple (but useless) alternative:
This form certainly has nicer values in the matrix. However, the
solution

might still be considered feasible as the
bounds on variables and constraints might be violated within the
tolerances. A better alternative is to reformulate
as
where

. In this setting, the most negative values for

which might be considered feasible would be

, and for
the original

variable it would be

, which is a clear
improvement over the original situation.