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From: "Bruno Luong" <b.luong@fogale.findmycountry>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Non-linear optimization
Date: Tue, 5 Mar 2013 07:26:08 +0000 (UTC)
Organization: FOGALE nanotech
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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