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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: 9,822
Registered: 7/26/08
Re: Non-linear optimization
Posted: Mar 5, 2013 2:26 AM
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"Matt J" wrote in message <kh32ds$hrn$>...
> "Toan Cao" <> wrote in message
> If you know a global lower bound on F(x), say F_low, then the minimization problem is equivalent to
> min f(x)'.f(x)
> where
> f(x)=F(x)- f_low
> So, you could apply Levenberg-Marquardt and/or Gauss-Newton to the reformulated problem.

I don't think it is a good suggestion. (1) It make the code difficult to handle since f_low needs to be known. It squares the conditioning of the original problem, and thus all kinds of numerical difficulties become more prominent.

When levenberg-Markquardt or pseudo-newton method is developed, f(x) is usually taken as the local Jacobian of F. And this approximation is generally known and studied. The approximation can be applied on any F (only assumed to be differentiable).


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