Optimize.fmin does not find minimum on well-behaved continuous function

Question

I'm trying to find the minimum on the following function:

Here's the call:

>>> optimize.fmin(residualLambdaMinimize, 0.01, args=(u, returnsMax, Param, residualLambdaExtended),
                               disp=False, full_output=True, xtol=0.00001, ftol = 0.0001)
Out[19]: (array([ 0.0104]), 0.49331109755304359, 10, 23, 0)
>>> residualLambdaMinimize(0.015, u, returnsMax, Param, residualLambdaExtended)
Out[22]: 0.46358005517761958
>>> residualLambdaMinimize(0.016, u, returnsMax, Param, residualLambdaExtended)
Out[23]: 0.42610470795409616

As you can see, there's points in the direct neighborhood which yield smaller values. Why doesn't my solver consider them?

Answer 1

Here is a suggestion which may help you debug the situation. If you add something like data.append((x, result)) to residualLambdaMinimize , you can collect all the points where optimize.fmin is evaluating residualLambdaMinimize :

data = []
def residualLambdaMinimize(x, u, returnsMax, Param, residualLambdaExtended):
    result = ...
    data.append((x, result))
    return result

Then we might be better able to understand what fmin is doing (and maybe reproduce the problem) if you post data without us having to see exactly how residualLambdaMinimize is defined.

Moreover, you can visualize the "path" fmin is taking as it tries to find the minimum:

import numpy as np
import scipy.optimize as optimize
import matplotlib.pyplot as plt

data = []

def residualLambdaMinimize(x, u, returnsMax, Param, residualLambdaExtended):
    result = (x-0.025)**2
    data.append((x, result))
    return result

u, returnsMax, Param, residualLambdaExtended = range(4)
retval = optimize.fmin(
    residualLambdaMinimize, 0.01, 
    args=(u, returnsMax, Param, residualLambdaExtended),
    disp=False, full_output=True, xtol=0.00001, ftol = 0.0001)

data = np.squeeze(data)
x, y = data.T
plt.plot(x, y)
plt.show()