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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."

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