NLopt on the Rosenbrock function

Here is our first attempt at using nlopt on the Rosenbrock banana function which we
used last time using the Nelder-Meade solver implemented in scipy.optimize.fmin function

import nlopt
from numpy import *

def nlopt_rosen_fg(x, grad):
   return sum(100.0*(x[1:]-x[:-1]**2.0)**2.0 + (1-x[:-1])**2.0)


x0 = [1.3, 0.7, 0.8, 1.9, 1.2]
n    = len(x0)
grad = array([0] * n)

opt = nlopt.opt(nlopt.LN_NELDERMEAD, len(x0))
opt.set_min_objective(nlopt_rosen_fg)
opt.set_xtol_rel(1.0e-4)
opt.set_maxeval(500)
opt.optimize(x0)
opt_val= opt.last_optimum_value()
opt_result = opt.last_optimize_result()
print 
print opt_val
print x0
print opt_result

When the above program runs, the following output is obtained:

python rosenbrock-nlopt.py 

1.22270197534e-08
[1.3, 0.69999999999999996, 0.80000000000000004, 1.8999999999999999, 1.2]
4

The return code of 4 means that the xtol has been achieved. We notice that the optimized vector is far from all ones although the function value is near zero. Doubtless we still have much to learn in using nlopt for this simple optimization without derivatives and we welcome any insightful remarks.

In the docs, it is not stated how many function evaluations were actually taken at the point of termination. It is obvious but the optimal vector is the final value of the initial vector variable.