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From "Jurgen Tas (JIRA)" <j...@apache.org>
Subject [jira] Commented: (MATH-246) Simplex Method Implementation
Date Sun, 07 Feb 2010 15:18:28 GMT

    [ https://issues.apache.org/jira/browse/MATH-246?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12830716#action_12830716
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Jurgen Tas commented on MATH-246:
---------------------------------

Benjamin thank you for your reaction. However, I am not entirely sure about the use of this
epsilon. What is e.g. the relationship  with the status of the system (i.e.ill-conditioning
of the constraints matrix) of constraints and the value of epsilon? A small test I did this
week was the following:

max (x1 + x2) subject to the following constraints:

x1 + x2 = 1
(1+delta)x1 + (1-delta)x2 = 1
x1, x2 >= 0

with delta a small number. The matrix A = [ (1,1), (1+eps, 1-eps)] is ill-conditioned. The
epsilon in the simplex algorithm was set on the the default value of 1e-6. I found that for
values of delta larger than 1e-6 the simplex algorithm provided an answer that does not obey
all the constraints. If delta was smaller than epsilon the solution obeyed all the constraints.


Any idea what this effect is, and how I can detect this for a general problem?

Regards,

Jurgen

> Simplex Method Implementation
> -----------------------------
>
>                 Key: MATH-246
>                 URL: https://issues.apache.org/jira/browse/MATH-246
>             Project: Commons Math
>          Issue Type: New Feature
>            Reporter: Benjamin McCann
>            Assignee: Luc Maisonobe
>             Fix For: 2.0
>
>         Attachments: newfiles.zip, simplex.patch, SimplexSolverTest.patch, SimplexTableau.patch,
test.patch
>
>
> I've created an implementation of the Simplex algorithm for optimizing systems of constrained
linear equations that I'd like to contribute.

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