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Avoid hiding large coefficients
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:
![<span>$</span>\begin{array}{rcl}
x - 10^{6} y &\geq& 0 \
y&\in&[0,10]
\end{array}<span>$</span>](https://www.gurobi.com/wp-content/plugins/hd_documentations/documentation/9.5/refman/img333.svg?x61957)
![<span>$</span>\begin{array}{rcl}
x - 10 y_1 &\geq& 0\
y_1 - 10 y_2 &=& 0\
y_2 - 10 y_3 &=...
...y_4 &=& 0\
y_4 - 10 y_5 &=& 0\
y_5 - 10 y &=& 0\
y&\in&[0,10]
\end{array}<span>$</span>](https://www.gurobi.com/wp-content/plugins/hd_documentations/documentation/9.5/refman/img334.svg?x61957)
might still be considered feasible as the
bounds on variables and constraints might be violated within the
tolerances. A better alternative is to reformulate
![<span>$</span>\begin{array}{rcl}
x - 10^{3} y' &\geq& 0 \
y'&\in&[0,10^4]\
\end{array}<span>$</span>](https://www.gurobi.com/wp-content/plugins/hd_documentations/documentation/9.5/refman/img336.svg?x61957)
. 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.
Next: Dealing with big-M constraints Up: Tolerances and user-scaling Previous: Advanced user scaling
