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## Re: [Help-glpk] Why would fixed constraints lead to infeasibility?

**From**: |
Michael Hennebry |

**Subject**: |
Re: [Help-glpk] Why would fixed constraints lead to infeasibility? |

**Date**: |
Mon, 21 Sep 2009 20:41:49 +0400 |

On Mon, 21 Sep 2009, Sam Seaver wrote:
>*> GLPK does allow one to fix variables.*
>*> I suspose it's *possible* that telling it a fixed "variable" is*
>*> double bounded instead of fixed might cause it to do the wrong thing.*
>*> Probably the difficulty is elsewhere.*
>*> Is your problem almost infeasible?*
>
>* How do I determine the 'almost' part?*
With difficulty.
Here is a possiblity:
Scratch the old objective.
Replace it with maximize slack.
Leave equalities alone.
Replace Ax>=b with slack<=Ax-b.
Replace Ax<=b with slack<=b-Ax.
Mathematically, for the original problem to be feasible,
the optimal of the new problem must be non-negative.
If it's small, the original problem is almost infeasible.
Scaling could affect both the difficulty in solving
the original and the optimum of the new problem.
--
Michael address@hidden
"Pessimist: The glass is half empty.
Optimist: The glass is half full.
Engineer: The glass is twice as big as it needs to be."