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Re: [Help-gsl] Nonlinear Solver With Bounds

From: Barrett C. Foat
Subject: Re: [Help-gsl] Nonlinear Solver With Bounds
Date: Fri, 14 Sep 2007 08:30:10 -0500
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Hi Eskandar,

You can impose constraints on model parameters by defining auxiliary 
functions. For example if you want a parameter b to always be positive, 
you add it to the function as c^2 and then after the algorithm converges 
on a value (positive or negative) for c, you just square it to get your 
final value of b. Likewise, you can impose any arbitrary range using sin 
or cos. For example if you want values of b only between 0 and 1, you can 
represent it by (0.5 * (cos(c) + 1)). No matter what value c takes during 
the minimization, b = (0.5 * (cos(c) + 1)) is always between, 0 and 1 

Sorry, I'm not familiar with the PORT library.

Barrett Foat

On Thursday 13 September 2007 17:04, Eskandar Ensafi wrote:
> Hi,
> I would like to use the functions defined in
> "gsl_multifit_nlin.h" to solve nonlinear least-squares
> and general nonlinear minimization problems.  However,
> I do not see a way to impose constraints (simple
> bounds) on the model parameters (independent
> variables).  This is particularly important in
> problems where one or more model parameters must
> always be positive, or if a weight parameter must
> always be between 0 and 1.  How can this problem be
> addressed in the current version of GSL?
> Also, for those of you familiar with the PORT Library
> <>, how does
> GSL's nonlinear solver compare to the PORT versions in
> terms of robustness?  I am specifically referring to
> the PORT routines DN2FB and DN2GB, which were based on
> NL2SOL, an adaptive nonlinear least-squares algorithm
> (ACM TOMS Algorithm 573).
> Thanks!
> Eskandar
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