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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 4:36 PM
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"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <khavr6$imm$1@newscl01ah.mathworks.com>...
> "Matt J" wrote in message <khaui3$efe$1@newscl01ah.mathworks.com>...
>

> >
> > I'm not sure what link with quasi-Newton that you're referring to. If you're saying that
> >
> > (H+lambda*I) x=gradient
> >
> > is an LM generalization of Newton's method,

>
> Quasi-Newton -> Replace Hessian by an appoximation of it, usually based from the first derivative, such as BFGS formula or H ~ J'*J in the least square cost function, where J is the Jacobian of the model.
>

> >then yes, I'm sure Newton-LM would converge faster, however each iteration looks costly. You would have to know the minimum eigenvalue of H in order to make (H+lambda*I) positive definite.
>
> Both BFGS and J'*J approximation provide quasi convex quadratic approximation. Therefore there is no need to bother with such detail about positiveness.

========

That much, I understand. Maybe I didn't understand what you meant by quasi-Newton being "quasi-efficient". It looks like finding lambda for quasi-Newton-LM would be much more efficient than for true Newton-LM.



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