Re: Interval hardware and existing practice
Dear Mr. Hayes,
> In my view, the problem with decorated intervals is they don't appear to
> provide any benefit or function that can't be achieved more simply and
> efficiently with a few standardized NaIs, which would retrofit very nicely
> into existing hardware.
> I think those in favour of decorated intervals need to show why they are
> absolutely necessary;
> even if this can be done, it should also be explained
> why we CAN'T also have NaIs for the branch-and-bound algorithms.
Paving C you have computed using NaI is not at all satisfactory from
the point of view of branch and prune algorithms. The art of designing
constraints branch and prune (and branch and bound) algorithms is
exactly to avoid this kind of effect, i.e. avoid bisections that
refine a part of the search space which contains no solutions, and
thus which could be rejected without any refinement!
I beleive we should stick to the well accepted definition
(1) f(xx) = IntervalHull { f(x) in R : x in (xx intersection Df) }
Couldn't we requiere two aritmetics in the standard? One optimized
that implements (1), and another that include decorations (and thus
would be less performant)?
Alexandre Goldsztejn
--
Dr. Alexandre Goldsztejn
CNRS - University of Nantes
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