Re : problem with NonlinearFit

• To: mathgroup at smc.vnet.net
• Subject: [mg4759] Re : [mg4705] problem with NonlinearFit
• From: erase at grenet.fr
• Date: Fri, 13 Sep 1996 13:54:46 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Brian O'NEILL" <oneill at iiasa.ac.at> wrote

----------------
I am having the following problem with the NonlinearFit function, and would
appreciate any tips you might have. (I have appended sample Mathematica code
below.)

My goal is to fit a non-monotically decreasing time series with a
monotonically decreasing function (specifically, a sum of decaying
exponenitials plus a constant).  I am approaching the problem by using
NonlinearFit and specifying a general functional form, then attempting to
constrain the search to non-negative coefficients and non-positive
exponents.  However, in general I have run into the following problems:

(1) NonlinearFit will accept parameter specifications of the form {x,xo}, or
of the form {x,minx,maxx}, but not of the form {x,xo,xmin,xmax}.  This means
I can constrain the variables, but I can't start from different points to
test robustness.

(2)The routine stops when it tries to search outside the constraints instead
of continuing the search in a different direction, so that it is important
to be able to specify different initial values to look elsewhere.
-------------------------------

May be it is possible to try a classical trick  (Walter et Pronzato
Identification de modeles parametriques, Masson, Paris, 1994, p. 67, but it
is in french !)

- In the general functional fn change non-negative parameter ai by  Exp[Ai]
- Find Ai by fiting data with parameter specification of the form {Ai,Ai0}
- find ai with ai =3D Exp[Ai] , so 0 < ai < Infinity

Hope this works

jpd

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