Re: Branch & bound for not everywhere defiend constraints

[Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>]

Nate Hayes schrieb:
> Arnold Neumaier wrote:

> > The problem is that one cannot know beforehand when the function is
> > outside its domain, once the domain is not a simple box, and one
> > does not know beforehand whether the information in the result is
> > useful or not.
>
> No. In the Paving B example, it is known before the branch-and-bound
> algorithm begins that the interval result will never be of any use if a
> domain violation occurs (with exception, see below).

If this is known beforehand, one can remove that part from the box
by prior bisections in the corresponding variables.
Then there is no issue at all with domain questions, and the algorithm
improves in efficiency. (For without these well-targeted bisection, the 
number of bisections to be made can only increase, and one wastes for
each needed bisection one calculation that returns a NaI.)


Arnold Neumaier