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Re: [Help-glpk] solve, add rows, resolve

From: Andrew Makhorin
Subject: Re: [Help-glpk] solve, add rows, resolve
Date: Thu, 18 May 2006 12:06:06 +0400

> I agree with your evaluation.  Removing a basic column is not
> intelligent behavior for a user, so you should not have to go to great 
> lengths to support it.
> However, it would be nice if GLPK would resolve from scratch in this 
> case rather than aborting with an error (perhaps with a message 
> indicating that it is making a new basis).
> Would you be willing to make that change?  If you would like, I can try 
> to submit a patch.

I think the patch is not needed. The application program only needs
to check the basis and repair it if necessary:

   ret = lpx_simplex(lp);
   if (ret == LPX_E_FAULT)
   {  ret = lpx_warm_up(lp);
      if (ret == LPX_E_BADB)
      {  /* the basis is invalid; build some valid basis */
         ret = lpx_simplex(lp);

However, using lpx_adv_basis (or lpx_cpx_basis) is not a good
idea to repair the basis, because these routines do not take into
consideration current row and column statuses. There should be a
more specialized routine which, for example, adjusts the basis
to make the number of basic variables be equal to the number of
rows, calls lpx_warm_up, and if the basis matrix is singular,
replaces linearly dependent basic columns by unity columns of
auxiliary (i.e. slack/artificial) variables.

Andrew Makhorin

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