Fri Nov 21 08:12:26 CST 2008

```Thanks Nils.  I will install and investigate openopt.  This looks like a
very exciting development.

Others:  I would still like to understand why I am not being successful with
scipy.optimize.  Was I wrong to think that NCG could handle my constraint,
even when I am providing the Hessian matrix?

Thanks

Gísli

On Fri, Nov 21, 2008 at 1:16 PM, Nils Wagner
<nwagner@iam.uni-stuttgart.de>wrote:

> On Fri, 21 Nov 2008 12:10:41 +0000
>
>> Hello all.
>>
>> I am a relatively new user of python and scipy and I have been trying
>> out scipy's optimization facilities.  I am using scipy version 0.6.0,
>> as distributed with Ubuntu 8.04.
>>
>> My exploration has centered around the minimization of x*x*y, subject
>> to the equality constraint 2*x*x+y*y=3.  In my experience, this
>> problem is solved by introducing a Lagrange multiplier and minimizing
>> the Lagrangian:
>>
>> L = x*x*y - lambda * ( 2*x*x+y*y-3 )
>>
>> I have had no problem finding the desired solution via Newton-Raphson
>> using the function and its first and second derivatives:
>>
>> import scipy.optimize as opt
>> import numpy
>> import numpy.linalg as l
>>
>> def f(r):
>>   x,y,lam=r
>>   return x*x*y  -lam*(2*x*x+y*y-3)
>>
>> def g(r):
>>   x,y,lam=r
>>   return numpy.array([2*x*y-4*lam*x, x*x-2*lam*y, -(2*x*x+y*y-3)])
>>
>> def h(r):
>>   x,y,lam=r
>>   return numpy.mat([[2.*y-4.*lam, 2.*x,
>> -4.*x],[2.*x,-2.*lam,-2.*y],[-4.*x,-2.*y,0.]])
>>
>> def NR(f, g, h, x0, tol=1e-5, maxit=100):
>>   "Find a local extremum of f (a root of g) using Newton-Raphson"
>>   x1 = numpy.asarray(x0)
>>   f1 = f(x1)
>>   for i in range(0,maxit):
>>       dx = l.solve(h(x1),g(x1))
>>       ldx = numpy.sqrt(numpy.dot(dx,dx))
>>       x2 = x1-dx
>>       f2 = f(x2)
>>       if(ldx < tol): # x is close enough
>>           df = numpy.abs(f1-f2)
>>           if(df < tol): # f is close enough
>>               return x2, f2, df, ldx, i
>>       x1=x2
>>       f1=f2
>>   return x2, f2, df, ldx, i
>>
>> print NR(f,g,h,[-2.,2.,3.],tol=1e-10)
>>
>> My Newton-Raphson iteration converges in 5 iterations, but I have had
>> no success using any of the functions in scipy.optimize, for example:
>>
>> print opt.fmin_bfgs(f=f, x0=[-2.,2.,3.], fprime=g)
>> print opt.fmin_ncg(f=f, x0=[-2.,2.,3.], fprime=g, fhess=h)
>>
>> neither of which converges.
>>
>> I am beginning to suspect some fundamental misunderstanding on my
>> part.  Could someone throw me a bone?
>>
>> Best regards
>>
>>  Gísli
>> _______________________________________________
>> SciPy-user mailing list
>> SciPy-user@scipy.org
>> http://projects.scipy.org/mailman/listinfo/scipy-user
>>
>
> Please find enclosed an untested implementation using openopt.
>
> Cheers,
>          Nils
>
>
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>
>
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