[SciPy-user] Usage of fmin_tnc and fmin_l_bfgs_b

[Nils Wagner]

On Fri, 15 Sep 2006 08:59:09 -0700
  "Xiaojian Wang" <wangxj.uc at gmail.com> wrote:
> Thanks Nils,
> 
> yes, fmin_cobyla  can handle the general constraints, 
>however I also still
> don't know how to
> write the constraints: "a list of callable function" 
>cons
> and there are no examples in this optimize module!, I 
>also appreciate any
> helps from any of you.
> 
> for fmin_l_bfgs_b, see examples in this module, I have 
>run this module
> without difficulty including
> lower and upper boundary for each design variables to 
>solve my problems.
> 
> Xiaojian
> 
> 
> 
> 
> 
> On 9/15/06, Nils Wagner <nwagner at iam.uni-stuttgart.de> 
>wrote:
>>
>> 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
>> >
>> > _______________________________________________
>> > SciPy-user mailing list
>> > SciPy-user at scipy.org
>> > http://projects.scipy.org/mailman/listinfo/scipy-user
>> >
>> Sorry for replying to myself.
>>
>> 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
>>
>>
>> _______________________________________________
>> SciPy-user mailing list
>> SciPy-user at scipy.org
>> http://projects.scipy.org/mailman/listinfo/scipy-user
>>

You can use something like this

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

xopt = 
optimize.fmin_cobyla(F_p,x_0,cons=(cons1,cons2,cons3,cons4,),rhobeg=1.0,rhoend=1.e-7,maxfun=9000)
  
Nils