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Topic: Non-linear optimization
Replies: 32   Last Post: Mar 8, 2013 2:22 AM

 Messages: [ Previous | Next ]
 Matt J Posts: 4,997 Registered: 11/28/09
Re: Non-linear optimization
Posted: Mar 6, 2013 5:56 PM

"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <kh8g3b\$p6i\$1@newscl01ah.mathworks.com>...
> "Matt J" wrote in message <kh8dvs\$imu\$1@newscl01ah.mathworks.com>...
>

> >
> > But yes, the above is equivalent to minimizing F(x). That's what we want. Now, however, you can feed f(x) to LSQNONLIN and run its Levenberg-Marquardt routine.

>
> And in what sense this contortion supposes to do any good?
>
> The Gauss-Newton approximation of the square-root will certainly less accurate than working with F directly. Especially when the lower-bound is careless chosen.

=================

It was never really about doing any "good". It was about fulfilling the OP's request. :-)

The OP wanted a way to apply Gauss-Newton to this problem and I, at least, don't see any other way. Granted, Gauss-Newton would probably do badly with a poorly chosen lower bound, but with some tuning, a tighter bound might be identifiable. For example, one could update the optimization with increasing f_low until a solution with F(x)-f_low close to zero was found. The OP has also revealed that many terms in his cost function are already squares. It's only the non-square terms that require a lower-bound estimated, so that would probably help to make a tight f_low identifiable.

As for Levenber-Marquardt, it should still converge under this scheme, though perhaps slowly. Working with F directly would without question be better, but then you have to code it yourself. I have searched for general Levenberg-Marquardt routines on the FEX and didn't find them. :-(

Date Subject Author
3/4/13 Toan Cao
3/4/13 Steven Lord
3/4/13 Toan Cao
3/5/13 Steven Lord
3/5/13 Toan Cao
3/6/13 Matt J
3/6/13 Matt J
3/6/13 Toan Cao
3/6/13 Matt J
3/4/13 Matt J
3/4/13 Toan Cao
3/5/13 Matt J
3/5/13 Bruno Luong
3/6/13 Matt J
3/6/13 Bruno Luong
3/6/13 Matt J
3/6/13 Bruno Luong
3/6/13 Matt J
3/6/13 Bruno Luong
3/6/13 Matt J
3/7/13 Bruno Luong
3/7/13 Matt J
3/7/13 Bruno Luong
3/7/13 Matt J
3/7/13 Bruno Luong
3/7/13 Matt J
3/7/13 Bruno Luong
3/8/13 Matt J
3/8/13 Bruno Luong
3/7/13 Toan Cao
3/7/13 Matt J
3/7/13 Toan Cao
3/7/13 Matt J