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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: 4,997
Registered: 11/28/09
Re: Non-linear optimization
Posted: Mar 7, 2013 3:50 PM
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"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <kh9it4$qg1$>...
> "Matt J" wrote in message <kh8skk$s6c$>...

> > Bear in mind also that generic LM doesn't use the Jacobian of the cost function F(x), but rather the Hessian of F, or equivalently the Jacobian of F's gradient. This not only means a possibly intensive Hessian calculation, but also when you solve the update equation
> What you pointed out is the difference between Quasi-Newton and Newton. True both can be implemented with LM.
> In practice quasi-Newton is quasi sufficient.


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, 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.

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