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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