MMA cycles between two iterates

[jmlarson1]

When running MMA on a 2-dimensional test function, I see that it fails to converge, but rather bounces between two points indefinitely. MMA is at a local solution, but has not identified it as such.

Reproducing code example:

import numpy as np
import nlopt

np.set_printoptions(precision=16)
def six_hump_camel_func(x):
    x1 = x[0]; x2 = x[1]

    term1 = (4-2.1*x1**2+(x1**4)/3) * x1**2;
    term2 = x1*x2;
    term3 = (-4+4*x2**2) * x2**2;

    return  term1 + term2 + term3

def six_hump_camel_grad(x):
    x1 = x[0]; x2 = x[1]; grad = np.zeros(2)

    grad[0] = 2.0*(x1**5 - 4.2*x1**3 + 4.0*x1 + 0.5*x2)
    grad[1] = x1 + 16*x2**3 - 8*x2

    return grad

def objective(x,grad):

    f = six_hump_camel_func(x)
    grad[:] = six_hump_camel_grad(x)
    print(x)
    return f

opt = nlopt.opt(nlopt.LD_MMA, 2)
opt.set_min_objective(objective)
opt.set_lower_bounds(-np.array([3,2]))
opt.set_upper_bounds(np.array([3,2]))

x = opt.optimize([-1.64574396,  0.85195592])

Output:

[-1.64574396  0.85195592]
[-3.                -0.265038270143849]
... after a few dozen iterations ...
[-1.7036067193868951  0.7960835871353801]
[-1.7036067193868951  0.7960835871353804]
[-1.7036067193868951  0.7960835871353801]
[-1.7036067193868951  0.7960835871353804]
... keeps repeating the last two points ...

Scipy/Numpy/Python/NLopt version information:

>>> import scipy, numpy, nlopt; print(scipy.__version__, numpy.__version__, sys.version_info, nlopt.__version__)
1.1.0 1.14.3 sys.version_info(major=3, minor=6, micro=5, releaselevel='final', serial=0) 2.4.2

[stevengj]

You haven't set any stopping criteria?

[jmlarson1]

Is there no default stopping criteria?

[stevengj]

Nope. Sometimes it will stop if it can detect that the solution is at the limits of roundoff error, but not all algorithms implement this check.

[rsln-s]

Default stopping criteria would be nice to have. I've experienced the same issue.

Maybe this could be reclassified as a feature request?