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Topic: Non-linear optimization
Replies: 32   Last Post: Mar 8, 2013 2:22 AM

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Matt J

Posts: 4,994
Registered: 11/28/09
Re: Non-linear optimization
Posted: Mar 7, 2013 5:39 PM
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> >It looks like finding lambda for quasi-Newton-LM would be much more efficient than for true Newton-LM.
>
> Not sure I understand your statement. In LM method, finding lambda is based on the same empirical rules that works equally well regardless which the Hessian approximation or true Hessian is chosen.

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I don't see how that can be. For non-convex functions and non-posdef Hessians, an empirically chosen lambda could easily leave H+lambda*I singular, or at least, not positive definite and therefore non-descending. You would have to choose lambda>=min(eig(H)) to be sure that didn't happen, and that would require an eigen-analysis of H.



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