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Re: [Help-glpk] binary boolean

From: Michael Hennebry
Subject: Re: [Help-glpk] binary boolean
Date: Sun, 6 May 2012 00:33:10 -0500 (CDT)
User-agent: Alpine 1.00 (DEB 882 2007-12-20)

On Sat, 5 May 2012, Andrew Makhorin wrote:

3. Yet another description (as pointed out by Erwin and Michael)

  z >= x

  z >= y

  z <= x+y

  It is a good description, because all inequalities are facet-defined
  (until the mip instance includes other constraints).

Together with z<=1, it is *the* sensible description.
There are no other facets.
In general, { (x, y, f(x,y)) : (x, y) in {0, 1}**2 }
has precisely four facets.

Since their bounds are not facets, but are implied by facets,
it might be useful to require that x and y never be non-basic.
Likewise, z should not be non-basis at zero.

The situation is more complicated for larger numbers of variables.

Michael   address@hidden
"On Monday, I'm gonna have to tell my kindergarten class,
whom I teach not to run with scissors,
that my fiance ran me through with a broadsword."  --  Lily

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