root/PythonPackages/OpenOpt/openopt/doc/restricted_dom.py

"""
Some non-linear functions have much more restricted dom than R^nVars.
For example F(x) = log(x); dom F = R+ = {x: x>0}

For optimization solvers it is wont to expect user-povided F(x) = nan if x is out of dom.

I can't inform how successfully OO-connected solvers
will handle a prob instance with restricted dom
because it seems to be too prob-specific

Still I can inform that ralg handles the problems rather well
provided in every point x from R^nVars at least one ineq constraint is active
(i.e. value constr[i](x) belongs to R+)

Note also that some solvers require x0 inside dom objFunc.
For ralg it doesn't matter.
"""

from numpy import *
from openopt import NLP

n = 100
an = arange(n) # array [0, 1, 2, ..., n-1]
x0 = n+15*(1+cos(an))

f = lambda x: (x**2).sum() + sqrt(x**3).sum() 
df = lambda x: 2*x + 1.5*x**0.5

lb = zeros(n)
solvers = ['ralg']
#solvers = ['ipopt']
for solver in solvers:
    p = NLP(f, x0, df=df, lb=lb, xtol = 1e-6, iprint = 50, maxIter = 10000, maxFunEvals = 1e8)
    #p.checkdf()
    r = p.solve(solver)
# expected r.xf = small values near zero