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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
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> (H+lambda*I) x=gradient
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> 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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