Subject: optimization with constraints

From: [email-masked] (Bert te Velde)
Date: Thu, 23 Mar 1995 13:35:14 +0100

Dear Antonio (CCL),

>I am trying to do a non linear least squares fit,
>using a Marquardt type algoritm, but I need to restrict some
>parameters to make my function behaves correctly.
>Is available any program to constrain parameters to be positive?

formulate your problem with transformed parameters, such that
p_new = ln(p_old)
optimize p_new (without constraints) and obtain your original parameter (p_old) as
p_old = exp(p_new)

(this is just one of the many transformations that map {-inf,+inf} onto {0,+inf}.
Any other transformation that does the same might be used equally well. Sometimes the nature of the problem suggests a particular transformation.
The choice of transformation may affect the efficiency of the optimization algorithm)

bye

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Bert te Velde                       SCIENTIFIC COMPUTING & MODELLING
phone:  +31-20 44 47625 (direct)    Vrije Universiteit, Theor. Chemistry
                  47644 (secr.)     De Boelelaan 1083
fax     +31-20-44 47643             1081 HV Amsterdam
e-mail: [email-masked]          The Netherlands
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