Scipy BasinHopping not returning correct global minima-CodePudding

I'm working with the following scipy code.

import numpy as np
from scipy.optimize import basinhopping

n_iter = 100 

@np.vectorize
def f(x):
    return ( x * np.sin(x)   2*x) ** 2

x0 = -6
minimizer_kwargs = {"method": "BFGS"}
ret = basinhopping(f, x0, minimizer_kwargs=minimizer_kwargs, niter=n_iter)

print("global minimum: x = %.4f, f(x0) = %.4f" % (ret.x, ret.fun))

The global minimum of this function is at 0, but this isn't what basin hopping returns. Depending on the start position x0, it returns different local minima - not the global one at 0. If we set x_0 = -6, it returns a minima at -7.7, if we set x0 = 1, then it returns a minima at 0, so on.

Why is it not returning the global minima? Why is it returning the local minimum closest to its start position?

CodePudding user response：

If you increase n_iter to 1000 it works!

The output is

"global minimum: x = 0.0000, f(x0) = 0.0000"

It is a stochastic algorithm and in this case it requires some more attempts, indeed using

import numpy as np
from scipy.optimize import basinhopping


while True:
    n_iter = 850 

    @np.vectorize
    def f(x):
        return ( x * np.sin(x)   2*x) ** 2

    x0 = -6
    minimizer_kwargs = {"method": "BFGS"}
    ret = basinhopping(f, x0, minimizer_kwargs=minimizer_kwargs, niter=n_iter)

    print("global minimum: x = %.4f, f(x0) = %.4f" % (ret.x, ret.fun))

prints

"""
global minimum: x = -7.7230, f(x0) = 60.6709
global minimum: x = -0.0000, f(x0) = 0.0000
global minimum: x = -0.0000, f(x0) = 0.0000
global minimum: x = 0.0000, f(x0) = 0.0000
global minimum: x = -0.0000, f(x0) = 0.0000
global minimum: x = 0.0000, f(x0) = 0.0000
global minimum: x = -0.0000, f(x0) = 0.0000
global minimum: x = -0.0000, f(x0) = 0.0000
global minimum: x = -0.0000, f(x0) = 0.0000
global minimum: x = -7.7230, f(x0) = 60.6709
...
"""

Not always the algorithm with n_iter=850 finds the global minimum.