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Re: Non-linear optimization
Posted:
Mar 5, 2013 2:26 AM
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"Matt J" wrote in message <kh32ds$hrn$1@newscl01ah.mathworks.com>...
> "Toan Cao" <toancv3010@gmail.com> 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).
Bruno
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