| Constrained Optimization routine [message #45252] |
Fri, 26 August 2005 07:01  |
Gianluca Li Causi
Messages: 21
Registered: August 2005
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Junior Member |
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Hi all,
I'm wondering if anybody knows an IDL routine to perform minimization
of a nonlinear function given functional constraints on the variables.
I mean: I would minimize a nonlinear F(x0,...,xn) subject to the
constraint G(x0,...,xn)=0, where G is another nonlinear function of the
same variables.
I know the very good TNMIN routine from Craig B. Markwardt, it can deal
very well with simple boundary constraints on each variable (e.g. xi >
low_boundary or xi < high_boundary), but it is not possible to define a
limit constraint which is a function of more variables.
Can anybody help me?
Thank you so much.
Gianluca
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| Re: Constrained Optimization routine [message #45328 is a reply to message #45252] |
Mon, 29 August 2005 10:26  |
James Kuyper
Messages: 425
Registered: March 2000
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Senior Member |
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Gianluca Li Causi wrote:
> Thanks James, I'd not tried it!
>
> I've done it now upon your suggestion: it really does what I've
> described, but I've realized that it does not work with my specific
> problem, probably because one of my boundary G functions is a discrete
> one!
> In fact i have to minimize F so that a continuous G1 constraint is
> satisfied AND a second discrete constraint, G2, (which is the number of
> local maxima of F, so an integer value) is fixed.
>
> Can you or anybody else suggest me a similar routine which also handle
> discrete functions?
Would it be feasible to iterate over the plausible values of the
discrete constraint, doing a seperate constrained minimization for
each, and then select the value that has the lowest minimum? It's a
brute force method, but it should work, if it doesn't overstrain your
system.
I've seen minimization routines that allowed you to specify a minimum
step size; by setting that step size to 1 for G2, you could get it to
handle this pretty automatically. Unfortunately, CONSTRAINED_MIN
doesn't seem to have this feature.
If the brute-force method is too expensive, you might try writing a
function that takes a single argument, which it rounds to the nearest
integer, and uses as the number of local maxima. It would call
CONSTRAINED_MIN to find the mimimizing combination of the other
variables for that number of maxima, returning the value of that
minimum. This is a one-dimensional function that can itself be minized
by a routine which does have a minimum step size that can be set to 1,
such as NEWTON(..., TOLX=1) or FX_ROOT(..., TOL=1).
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