help-glpk
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 From: Нестеренко Геннадий Витальевич Subject: RE: [Help-glpk] Hi: Question. Please help. Date: Tue, 29 Jul 2008 09:57:56 +0400

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-----Original Message-----
Sent: Friday, July 25, 2008 4:50 PM

> I am trying to use GLPK in a flux-balance analysis context in biology.
> Once the linear constraints are defined and maximization of the
> objective function is done, I often find that the solution contains too
> many changes across the free variable set, and I cannot change that many
> variables (over 1000 sometimes) for my engineering problem. I can at the
> most take care of say a 15-20. How can I restrict the number (not
> magnitude) of changes in the LP maximization?

You may try solving your problem in two stages as follows. On the first
stage you solve your original problem as usual. And on the second stage
you fix the objective function at the optimal value found on the first
stage (or limit it by some percentage of its optimal value) and then
minimize the sum of |b[i]|, where b[i] are free variables. In LP context
sum |b[i]| can be replaced by sum(b1[i] + b2[i]), where b1[i] and b2[i]
are non-negative, and b1[i] - b2[i] = b[i].

Sorry.. I've probably misunderstood this. Let's take
-3=5-8,
5>=0, 8>=0,
but
|-3|<>5+8

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