[SciPy-user] Question about scipy.optimize

[dmitrey]

Both fmin_bfgs and fmin_ncg expect objective function to be convex, 
while y*x^2 is not. I have no time & willing to dig more deeply for the 
solvers involved, problem and code mentione.
D.

Gísli Óttarsson wrote:
>
> 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 at iam.uni-stuttgart.de <mailto:nwagner at iam.uni-stuttgart.de>> 
> wrote:
>
>     On Fri, 21 Nov 2008 12:10:41 +0000
>      "Gísli Óttarsson" <gislio at gmail.com <mailto:gislio at gmail.com>> wrote:
>
>         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
>         _______________________________________________
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>
>
>     Please find enclosed an untested implementation using openopt.
>
>     Cheers,
>              Nils
>
>
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