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Recommended ranges for variables and constraints
Keeping the lessons of the previous section in mind, we recommended
that right-hand sides of inequalities representing physical quantities
(even budgets) should be scaled so that they are on the order of
or less. The same applies to variable domains, as variable
bounds are again linear constraints.
In the case of objective functions, we recommend that good solutions
should have an optimal value that is less than , and ideally
also above one (unless the objective coefficients are all zero). This is
because the OptimalityTol is used to ensure that reduced cost are close enough to zero. If coefficients are too large,
we again face difficulties in determining whether
an LP solution truly satisfies the optimality conditions
or not. On the other hand, if the coefficients are too
small, then it may be too easy to satisfy the feasibility
conditions.
The coefficients of the constraint matrix are actually more important than the right-hand side values, variable bounds, and objective coefficients mentioned here. We'll discuss those shortly.
Next: Improving ranges for variables Up: Tolerances and user-scaling Previous: Why scaling and geometry
