[Clp] Interpretation of solution variables beyond bounds

[Lou Hafer]

Alex,

> Sometimes CLP gives a solution where some variable values are beyond
> their bounds.
> Example below:
> 
> Maximize
> 1.2 x + 2.2 y
> Subject To
> eq1: 1.1 x + 2.1 y <= 11
> eq4: 1.4 x + 2.4 y <= 14
> eq6: 1.2 x + 2.2 y - z = 10
> eq5: z - t = 2.0000001
> Bounds
> x >= 0
> y >= 0
> z >= 0
> t >= 0
> End
> 
> Clp reports solution is optimal, but the resulting t is -1e-07 (beyond
> the limit t >= 0).
>
> [ ... ]
> 
> Is there some correct way of handling variables that are beyond
> variables?

The default primal feasibility tolerance is 1e-7, and the rhs of eq5
differs from 2.0 by the same value. The solution is correct within the
specified tolerance. Rescale the problem, or specify a smaller primal
feasibility tolerance.

						Lou