[SciPy-user] Optimization fmin_tnc with equality constraint

josef.pktd@gmai... josef.pktd@gmai...
Mon Apr 20 07:40:44 CDT 2009


On Mon, Apr 20, 2009 at 8:26 AM, Dave Hirschfeld
<dave.hirschfeld@gmail.com>wrote:

> Adrien Aulagnier <aaulagnier <at> gmail.com> writes:
>
> >
> > HelloSorry to disturb you. My question might be simple:The function to
> minimize is simply f (w) = w' *  Sigma * wwith w a vector and Sigma a
> square
> matrixThe constraints are : 0 <= w <= 1
> >  sum(w) = 1This last constraint is my problem.Could you give me some clue
> ?Thanks for your help
> >
> > _______________________________________________
> > SciPy-user mailing list
> > SciPy-user <at> scipy.org
> > http://mail.scipy.org/mailman/listinfo/scipy-user
> >
>
> This discussion may help:
>
> http://thread.gmane.org/gmane.comp.python.scientific.user/16180/focus=16187
>
>
For a constraint on a simplex, I have seen a multinomial logit, or dirichlet
(?) reparameterization  most often:

something like:
w_i = exp(wn_i)/(1+sum_i(exp(wn_i))  for i>0
w_i = 1/(1+sum_i(exp(wn_i)) for i=0

wn has length = len(w)-1

Josef
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