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## Re: [Help-glpk] binary boolean

**From**: |
Michael Hennebry |

**Subject**: |
Re: [Help-glpk] binary boolean |

**Date**: |
Fri, 4 May 2012 12:33:33 -0500 (CDT) |

**User-agent**: |
Alpine 1.00 (DEB 882 2007-12-20) |

On Fri, 4 May 2012, Andrew Makhorin wrote:

Since the conversion from mathematical formulation to constraints is
systematic , could this be added to marhprog?

No, it is not. There exist infinitely many mip descriptions of the same
integer set. Even z = x OR y can be formulated in infinitely many ways.

All the sensible ones are equivalent.
Even a function from two booleans to the reals will have a simple convex hull.
If full dimensional, the convex hull will be a tetrahedron.
If not, the function is linear.
More booleans would complicate matters.
The convex hull could still be achieved with
2**n additional continuous variables,
though making them binary would still be mathematically correct.
Without additional variables, one might have to sacrifice the convex hull,
but 2**(n+1) constraints would be sufficient
and could be systematically generated.
In this case, different systems might produce inequivalent constraints.
--
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

**[Help-glpk] binary boolean**, *Zvonko Bregar*, `2012/05/03`
**Re: [Help-glpk] binary boolean**, *Erwin Kalvelagen*, `2012/05/03`
**Re: [Help-glpk] binary boolean**, *Yaron Kretchmer*, `2012/05/03`
**Re: [Help-glpk] binary boolean**, *Andrew Makhorin*, `2012/05/04`
**Re: [Help-glpk] binary boolean**, *Yaron Kretchmer*, `2012/05/04`
**Re: [Help-glpk] binary boolean**, *Andrew Makhorin*, `2012/05/05`
**Re: [Help-glpk] binary boolean**, *Andrew Makhorin*, `2012/05/05`
**Re: [Help-glpk] binary boolean**, *Michael Hennebry*, `2012/05/06`
**Re: [Help-glpk] binary boolean**, *Andrew Makhorin*, `2012/05/05`
**Re: [Help-glpk] binary boolean**, *Yaron Kretchmer*, `2012/05/05`
**Re: [Help-glpk] binary boolean**,
*Michael Hennebry* **<=**