我在使用scipy的minimize()函数时遇到问题，并且我对优化的了解还不足以了解这里的问题。
我有一个调用scipy.optimize.minimize()的函数。当x0的数组大小大于1时，它可以很好地工作并为我提供所需的输出，但是当x0恰好为1时，它将失败。 documentation表示x0的大小必须为np.ndarray的{{1}}，但未指定其值应大于1，因此我认为可以。我的代码的较小版本以最佳值调用该函数：
(n,)现在，在未知最佳值的情况下，随机初始化import numpy as np
from scipy.optimize import minimize
def to_freq(*arrays):
# Better version of `convert_to_freq()`
out = []
for a in arrays:
converted = np.array([(x + i / len(a)) / (max(a)+1) for i, x in enumerate(a, start=1)])
out.append(converted)
return out
def likelihood(x, x_freq, expected, x_max):
# Better version, supports vectorisation
a = 2 * x * np.log(x_freq / expected)
b = 2 * (x_max - x) * np.log((1 - x_freq) / (1 - expected))
return a + b
def objective(x0, labels, a, b):
R = x0[labels=='R'].item()
a_c, b_c = np.cumsum(a), np.cumsum(b)
a_f, b_f = to_freq(a_c, b_c)
# Get the expected values for signals and noises
exp_a = ((1 - R) * b_f + R)[:-1]
exp_b = b_f[:-1]
# Compute the gsquared using the dual process model parameters
# Still getting runtime warnings about division. Function only works with numpy, so can't use math.
a_lrat = likelihood(x=a_c[:-1], x_freq=a_f[:-1], expected=exp_a, x_max=a_c.max())
b_lrat = likelihood(x=b_c[:-1], x_freq=b_f[:-1], expected=exp_b, x_max=b_c.max())
return sum(a_lrat + b_lrat)
# Observations
a = [508,224,172,135,119,63]
b = [102,161,288,472,492,308]
x0 = np.array([0.520274590415736]) # Optimal value for variable
labels = np.array(['R'])
# Gives correct iotimized value of 163.27525607890783
objective(x0, labels, a, b)
：
x0失败的优化结果是这样的：
x0 = np.random.uniform(-.5,0.5, len(labels)) # random initialization
# Without method='nelder-mead' occasionally gives correct value of fun, but frequently fails
opt = minimize(fun=objective, x0=x0, args=(labels, a, b), tol=1e-4)
print(opt)
但是如果我继续运行并随机设置初始值，它偶尔会吐出一个不错的结果：
fun: nan
hess_inv: array([[1]])
jac: array([nan])
message: 'Desired error not necessarily achieved due to precision loss.'
nfev: 336
nit: 1
njev: 112
status: 2
success: False
x: array([1034.74])
如果我在较大函数的 fun: 163.27525607888913
hess_inv: array([[4.14149525e-05]])
jac: array([-1.90734863e-05])
message: 'Optimization terminated successfully.'
nfev: 27
nit: 7
njev: 9
status: 0
success: True
x: array([0.52027462])
调用中指定了method='nelder-mead'（a solution to a possibly unrelated problem），它实际上也为我提供了预期的结果：
minimize()我不太了解实现此目标的最佳方法，因为我对优化非常缺乏经验。
[脚注]：最小化算法有时会尝试与我的函数不兼容的值（例如<0或> 1），并且对 final_simplex: (array([[0.52026029],
[0.52031204]]), array([163.27525856, 163.27527298]))
fun: 163.2752585612531
message: 'Optimization terminated successfully.'
nfev: 32
nit: 16
status: 0
success: True
x: array([0.52026029])
的调用最终会引发警告，但是我通常只是禁止这样做因为不管...似乎都能正常工作