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Re: [Bug-glpk] numerical instability (cycling?)

From: Andrew Makhorin
Subject: Re: [Bug-glpk] numerical instability (cycling?)
Date: Tue, 25 Aug 2009 16:49:40 +0400

> I am sure we both agree that getting into an infinite loop is not
> acceptable.

>> and applying geometric mean scaling makes the instance badly scaled.

> What is your opinion about the Curtis-Reid scaling algorithm?

I do not think that another scaling algorithm would help. The defect
is in the simplex solver.

>> However, a much better way is to replace tiny constraint coefficients
>> by exact zeros.

> How can i figure out what "tiny" is?

It depends on the instance's nature. I could suggest the following
criteria: a[i,j] is tiny if |a[i,j]| < 1e-8 * max|a[i,*]| assuming
that max|a[i,*]| is not very huge. For example, in the row:

1.23 x1 + 2.34 x2 + 3.45e-15 x3 + 4.56 x4 <= 5.67

constraint coefficient '3.45e-15' is tiny and should be replaced by
exact zero (or skipped at all).

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