[SciPy-user] Question about scipy.optimize

[Gísli Óttarsson]

Nuff said.

Thanks for setting me straight.

  Gísli

On Fri, Nov 21, 2008 at 2:19 PM, dmitrey <dmitrey.kroshko at scipy.org> wrote:

> 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
> >         _______________________________________________
> >         SciPy-user mailing list
> >         SciPy-user at scipy.org <mailto:SciPy-user at scipy.org>
> >         http://projects.scipy.org/mailman/listinfo/scipy-user
> >
> >
> >     Please find enclosed an untested implementation using openopt.
> >
> >     Cheers,
> >              Nils
> >
> >
> >     _______________________________________________
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> >     SciPy-user at scipy.org <mailto:SciPy-user at scipy.org>
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> >
> >
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