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Re: overflow question

On 05/10/2012 03:14 PM, Ralph Baker Kearfott wrote:


Ah, yes. That is certainly a valid point of view if the
function, say, has a limit or a solution at infinity; in
such cases, the best solution to the user's problem
might be for the person posing
the problem to map the domain into a finite, closed
interval, with one end point corresponding to infinity.
Otherwise excellent solvers such as Baron may perform very poorly on problems with very wide bounds, even if there is no solution at infinity, as their bisection rule uses the midpoint and hence spend most of their time searching very close to infinity although there is nothing to be found there.
At the ISMP 2012 conference in Berlin, I'll talk about precisely this kind of problem, and how to solve them efficiently. 


> Along these lines, a logical thing that comes to mind
> is to choose as midpoint of a positive semi-infinite interval
> the geometric mean of the lower bound and MAXREAL,
> to try to get the same number of floating point numbers
> in each half.
Yes, this is why a flmedian routine could be useful. Of course, using just flmedian has a corresponding problem for intervals containing zero. 


> However, I'm not saying we standardize
> this; this seems to be a research topic (minor or not).
> It is my personal opinion that we should standardize things
> that are already well-understood and for which there will
> be a universal benefit for everyone to be doing it the
> same way.
Yes. That's why the usual mathematical definitons of the midpoint (i.e., undefined for empty and unbounded), and a vanilla flmedian should be standardized, rather than newly invented halfbred rules that pollute the standard and won't have a future.