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On 03/20/2012 07:31 AM, John Pryce wrote:
Reminder: Quite a few people have argued in favour of a pragmatic "split" function that always does SOMETHING at Level 2, leaving "midpoint" free to be more mathematical and return NaN for intervals such as [0,inf] that have no midpoint at Level 1. IMHO this is a good idea. What does the group think? - For "split", if we decide to have it, what wins? Reproducibility or freedom? - Is this issue to be decided case by case, or should we have a general policy about it?
In this case, reproducibility is extremely important, as different branching behavior may mak a lot of difference to the performance, may even decide between success and failure.
On the other hand, there is no need to have a split in the standard. It would be arbitrary anyway, as there is no canonical way to define the split. (Note that until now, everyone had to write their own split, and it didn't stop anyone interested to write a B&B code.)
However, there is a _need_ to have a flMedian function (slitting at the median rounded to even of the set of floats in the interval) in the standard, as
-- its efficient implementation is not straightforward, -- it is 100% reproducible, and -- it may be profitably used in a B&B scheme, -- it will be best at least in certain cases. Arnold Neumaier