[Scipy-tickets] [SciPy] #1778: fmin_ncg fails at Rosenbrock

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Fri Nov 23 17:30:29 CST 2012

#1778: fmin_ncg fails at Rosenbrock
 Reporter:  unknown (google)  |       Owner:  somebody   
     Type:  defect            |      Status:  new        
 Priority:  normal            |   Milestone:  Unscheduled
Component:  scipy.optimize    |     Version:  devel      
 Keywords:  fmin_ncg          |  
 This ticket is about how a scipy nonlinear optimization procedure is
 failing to successfully find the minimum for a particular objective
 function given a particular initial guess, and I do not have any proof
 that this is actually a bug.

 The objective function is the bivariate Rosenbrock function
 http://en.wikipedia.org/wiki/Rosenbrock_function as defined in scipy and
 on wikipedia and in Rosenbrock's original paper.  The problematic initial
 guess is (-1.2, 1.0) which is the one used by Rosenbrock in his 1960
 publication.  For this starting guess, most of the scipy.optimize
 functions are able to find the minimum f(1,1)=0, (results not included
 here) but for some reason fmin_ncg fails, even though it has access to the
 function's gradient and hessian and the objective function is smooth with
 only a single local minimum.  Strangely, fmin_tnc successfully finds the
 optimum whereas fmin_ncg fails, even though the two algorithms are
 supposedly nearly the same (Newton conjugate gradient).

 >>> scipy.optimize.fmin_ncg(scipy.optimize.rosen, numpy.array([-1.2,
 1.0]), fprime=scipy.optimize.rosen_der, fhess=scipy.optimize.rosen_hess)
 Optimization terminated successfully.
          Current function value: 3.811010
          Iterations: 39
          Function evaluations: 41
          Gradient evaluations: 39
          Hessian evaluations: 39
 array([-0.95155681,  0.91039596])

 >>> scipy.optimize.fmin_tnc(scipy.optimize.rosen, numpy.array([-1.2,
 1.0]), fprime=scipy.optimize.rosen_der, disp=0)
 (array([ 1.00008039,  1.00016113]), 83, 1)

Ticket URL: <http://projects.scipy.org/scipy/ticket/1778>
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