SciPy通过＆＃39; eq＆＃39;最小化功能。约束但不是SLSQP算法（最好是GRG）

Question

我正在尝试使用NumPy和SciPy将Excel解算器转换为python，虽然我在技术上已经开始工作，但我在结果上遇到了轻微的差异。

通过公式输入样本数据：

array_1 = [
  0.0943417538897551,
  0.0799476059590533,
  0.0486689860368342,
  0.052434296201351 ,
  0.231614207638357,
  0.0808322159046283,
  0.0819215585688325,
  0.140991841045595,
  0.189247534431047
]

matrix_1 = [
  [0.0235147682238835,    0.0194641686338689,    0.0116344823277316,    0.0214041868628604,    0.010980242438382,     0.013085897256736,     0.0107928914491097,      -0.000350116147653561, 0.000323182155233255],
  [0.0194641686338689,    0.0227374787807333,    0.0147128129866735,    0.023168038099643,     0.00899606198312112,   0.0108035747784655,    0.00989996824509696,     -0.000271072225966624, 0.000337765823991017],
  [0.0116344823277316,    0.0147128129866735,    0.0265282312707786,    0.0140689757522423,    0.021443195995926,     0.0252024393105442,    0.0187159868856209,      0.000969972826332724,  -0.0000408711850838449],
  [0.0214041868628604,    0.023168038099643,     0.0140689757522423,    0.0288819629130722,    0.00890430456025532,   0.00987603454385401,   0.00914278195359995,     -0.000127719476583381, 0.000340663672172775],
  [0.010980242438382,     0.00899606198312111,   0.021443195995926,     0.00890430456025532,   0.029544562002381,     0.0314280240062057,    0.017176083705661,       0.00103517056623238,   0.0000307234067635423],
  [0.013085897256736,     0.0108035747784655,    0.0252024393105442,    0.00987603454385401,   0.0314280240062057,    0.0552293560476392,    0.0198882118118466,      0.000830285068544538,  -0.000328125366438888],
  [0.0107928914491097,    0.00989996824509696,   0.0187159868856209,    0.00914278195359995,   0.017176083705661,     0.0198882118118466,    0.0174188411860936,      0.000638033896492422,  -0.00000837412076787606],
  [-0.000350116147653561, -0.000271072225966624, 0.000969972826332724,  -0.000127719476583381, 0.00103517056623238,   0.000830285068544538,  0.000638033896492422,    0.00207309710065845,   0.00038309084175021],
  [0.000323182155233255,  0.000337765823991017,  -0.0000408711850838449, 0.000340663672172775, 0.0000307234067635422, -0.000328125366438888, -0.00000837412076787614, 0.00038309084175021,   0.000315889643542944]
]

user_input_number = 0.2 # fluctuates between 0 and 1

array_2 = [
  0.0555192520462957,
  0.0521964263617645,
  0.0727151670043896,
  0.0541841497069959,
  0.0797919901829936,
  0.0972924758058667,
  0.057466786568159,
  0.00266000663087858,
  0.000440591301372533,
]

我的计算函数如下所示：

def calculate(array_1):
  step_one = np.dot(np.dot(array_1, matrix_1), array_1)
  step_two = user_input_number * np.dot(array_2, array_1)
  return step_one - step_two 

# matrix_1, array_2, and user_input_number are defined outside of this scope

array_1数字的边界必须保持在0和1之间：

myBounds = ((0,1),(0,1),(0,1),(0,1),(0,1),(0,1),(0,1),(0,1),(0,1))

我需要传递约束，其中sum(array_1)等于1：

myConstraint = ({'type': 'eq', 'fun': lambda x:  1 - sum(x)})

所以我的SciPy minimize电话结束了这样的事情：

result = minimize(calculate, myArray, method="SLSQP", bounds=myBounds, constraints=myConstraint)

# 'SLSQP' is used because I read it is the only one that allows a constraint.

就像我提到的那样有效，但对于我们在Excel中得到的结果并不准确。

以下是解算器设置的屏幕截图：

你可以看到它使用的解决方法＆＃34; GRG Nonlinear＆＃34;但该选项不在可用方法下的minimize docs中。我看到了BFGS＆＃39;和＆＃39; L-BFGS-B＆＃39;建议哪些结果更接近，但我不能做一个很好的比较，因为它不允许将约束放在结果数组上。

我的整体问题是什么是复制＆＃34; GRG Nonlinear＆＃34;用约束最小化的方法？