How do you do it...?
Hi folks,
A question came up at dinner tonight. And it got me
thinking how an interval guy would solve it. I know
this is off topic to our current discussion but you
are the only interval guys I know. :-)
Suppose I have a potential function p(X) parameterized
by some multi-dimensional X (possibly many dimensions).
The parameters are further constrained by some vector
C(X) = 0 (also possibly many constraints).
The problem is to find the absolute minimum of the
potential subject to the constraints within which
there may be many local minima.
Now I suppose you could solve it by B&B or some
vector form of Newton's. That's not my question.
My question is: Do you work with the potential directly
or do you try to find zeros in its gradient? Actually,
I suppose that would be zeros in some norm on the
gradient.
The reason I ask is that it occurs to me that a typical
trial minimum would be in the interior of its bounding
box & therefore not something that is computed by
looking at the endpoints. And while zeros to the
gradient would also likely be in the interior, one
could instead "score" a bounding box by something like
the minimax of its endpoints.
Both are done in floating-point with good & bad aspects
to each. I'm curious what intervals brings to the table
that might be different in some qualitative fashion.
Anything?
I apologise for the digression.
Dan