[Raytrace] Re: Raytrace digest, Vol 1 #11 - 1 msg

[Tim Rickard]

It appears that the routines are simultaneously optimizing for multiple
parameters.
If so, the solution is probably non-linear, and most non-linear optimizers
run some risk of finding a local minimum (a shallow valley it cannot get out
of; as opposed the global minimum, the best solution). There is also the
possibility that it won't be able to converge on anything at all, or will
bump up against a boundary condition, which doesn't make it happy either.

Yes, starting value can be very critical for non-linear optimization.

The comments above apply generally, though I don't know the details of the
optimizer you are working with.  I hope this is useful.

Tim


> I went through Peter Smith's suggested sequence.  It worked well and was
> very instructive.
> I had no problem getting up to the Newtonian, Cassegrain, and thru the
> Dall-Kirkham.  However, the optimization routines (Hammer, Golbal)  would
> not converge when going from Dall-Kirkham to RItchey-Chretien when the
> secondary radius, primary and secondary conics were set to
> 'variable'.   After several attempts, I found that if I started from a
> Cassegrain and set the merit function to 'ptv spot size' rather than 'rms
> spot size', it converged.
> So I guess the lesson is that, in raytracing, it helps to know where to
> start.  Am I correct?
>
> Regards,
> P.C. Chen
>
>
>
>
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