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

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Bruno Luong

Posts: 8,706
Registered: 7/26/08
Re: Non-linear optimization
Posted: Mar 7, 2013 4:12 PM
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"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.

Those notions are well known in optimization discipline.

Bruno



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