[SciPy-user] Question about scipy.optimize
Gísli Óttarsson
gislio at gmail.com
Fri Nov 21 09:27:22 EST 2008
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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> >
> >
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