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Re: [Help-glpk] restarting GLPK with dual simplex

From: Andrew Makhorin
Subject: Re: [Help-glpk] restarting GLPK with dual simplex
Date: Mon, 3 Apr 2006 01:06:49 +0400

> When I run this I get the output below.  The first call to the (primal)
> simplex found an optimal solution at iteration 80153.  The second call,
> after moving some lower bounds from 0 to some positive integer, found a
> solution 7000 iterations later.

Ok. Now the second call to lpx_simplex provides reoptimization.

>   I guess that I expected the
> infeasibility to be reported as the dual infeasibility, but my current
> guess is that the reported infeasibility is always primal infeasibility
> even when running the dual simplex algorithm.  Is that correct?

That is correct. However, the infeasibility reported by the simplex
routines is an internal quantity intended for visual estimation only
unlike the objective value which always corresponds to the original
problem instance. For example, in the primal simplex it is a relative
quantity which is set to 1 at the beginning of the search, and in the
dual simplex it is a sum of infeasibilities for an internally scaled
(and possibly presolved) problem instance.

You can recognize which version of the simplex is used by the first
character displayed on the screen: '|' means the dual simplex while
' ' and '*' means the primal simplex (phase I and II respectively).

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