# [SciPy-user] Usage of fmin_tnc and fmin_l_bfgs_b

Nils Wagner nwagner at iam.uni-stuttgart.de
Fri Sep 15 03:45:44 CDT 2006

Nils Wagner wrote:
> Hi all,
>
> I would like to solve a constrained optimization problem with scipy.
> As far as I understand it there exists two possible functions for my
> problem in scipy - fmin_tnc and fmin_l_bfgs_b.
>
> The problem is given by
>
> min f(x)
>
> subjected to
>
> \theta_1 \le theta \le theta_2
>
>  and
>
>  r_1 \le r \le r_2
>
> where x is a vector \in \mathds{R}^{2n+1}.
>
> theta is the last entry in x.
>
> r = \| x[:2*n] \| = linalg.norm(x[:2*n])
>
>
> How do I specify the bounds for my problem ? I mean
> it's easy to define the bounds for the l a s t parameter (\theta) but
> I am at a loss how to formulate
> the bounds for x[0],...,x[2n-1] s e p a r a t e l y.
>
>     bounds  -- a list of (min, max) pairs for each element in x, defining
>                the bounds on that parameter. Use None for one of min or max
>                when there is no bound in that direction
>
> Any hint would be appreciated.
>
> Nils
>
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I guess I can use fmin_cobyla with the following constraints

cons1= x[-1]-\theta_1
cons2=\theta_2-x[-1]
cons3=linalg.norm(x[:2*n])-r_1
cons4=r_2-linalg.norm(x[:2*n])

Is that correct ? Is there a better way to implement the problem ?

Nils