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Stephen J. Herschkorn wrote:
Stephen J. Herschkorn wrote:
Jaime Gaspar wrote:
Can anyone tell how can I find the minima of a function like
f(x,y,z,w) = max{|x-y|,|x-z|,|x-w|,|y-z|,|y-w|,|z-w|}
over some subset of R^4?
If the subset can be described by linear equalities and inequalites,
you can formulate this as a linear program. If the subset is convex,
you want to look up convex programming. Note that in any case you
can still formulate the problem with a linear objective function.
Also note that if a minimum is attained on the subset, it must be at a
boundary point.
Oops. I take that back. Clearly, if there is a point where x = y = z
= w in the interior of the subset, the minimm occurs there. I was
thinking about the modified problem (with the linear objective function).
--
Stephen J. Herschkorn sjherschko@xxxxxxxxxxxx
Math Tutor in Central New Jersey and Manhattan
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