Re: [Help-glpk] binary boolean

[Michael Hennebry]

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