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我有一个简单的优化问题，使用一些特定的数据，使scipy.optimize.minimize忽略该tol参数。根据我的理解，从文档中tol确定“终止容差”，即目标函数接受的最大误差（我错了吗？）。然而，在下一个工作示例中，当tol设置为 0.1 或其他小数字时，即使目标函数 > ，优化也会以“优化成功终止”消息结束tol。这是 Scipy 方法中的错误还是我在这里误解了什么？

优化问题：我需要对 和 进行线性组合var1，var2它们是两个时间序列，通过参数Btd和缩放它们Bta。我需要线性组合的平均值接近目标值Target，一个标量。np.mean(Btd*var1 + Bta*var2)所以我只是最小化和之间的绝对差异Target。约束条件是比例系数必须大于 0，并且均值的比率np.mean(Btd*var1)/np.mean(Bta*var2)应近似于函数gi/(1-gi)，其中gi是区间 [0,1] 中的标量。

可重现的代码：

import numpy as np
import scipy.optimize as opt

# The data that exactly reproduce the error:
time = np.arange(1979,2011)
var2=np.array([ 88.95705521,  74.5398773 ,  72.08588957,  65.64417178,
        50.        ,  72.39263804,  77.3006135 ,  72.08588957,
        64.41717791,  96.62576687,  69.93865031,  84.96932515,
        86.50306748,  82.20858896,  80.98159509,  73.00613497,
        66.25766871,  67.48466258,  79.75460123,  65.64417178,
        70.24539877,  84.66257669,  76.3803681 ,  83.74233129,
        83.74233129,  78.2208589 ,  88.03680982,  87.73006135,
       100.        ,  71.16564417,  73.6196319 ,  85.58282209])
var1=np.array([300.        , 420.89552239, 333.58208955, 355.97014925,
       376.11940299, 510.44776119, 420.89552239, 434.32835821,
       333.58208955, 394.02985075, 523.88059701, 411.94029851,
       353.73134328, 434.32835821, 355.97014925, 398.50746269,
       476.86567164, 371.64179104, 445.52238806, 544.02985075,
       416.41791045, 427.6119403 , 541.79104478, 579.85074627,
       429.85074627, 414.17910448, 420.89552239, 528.35820896,
       577.6119403 , 490.29850746, 600.        , 454.47761194])
X=np.transpose([var1, var2])

# Global parameters
Target = 3.0
gi = 0.7

# This model is a simple linear combination of the two time series.
def MyModel(modelparams, X, gi):
    Bta, Btd = modelparams
    Eta = Bta*X[:,0]
    Etd = Btd*X[:,1]
    Etot = Eta + Etd
    return Etot, Eta, Etd

# Objective function
def Obj(modelparams):
    Bta, Bdt = modelparams
    Etot, Eta, Etd = MyModel([Bta, Bdt], X, gi)
    return abs(np.mean(Etot)-Target)

# Ratio constraint
def Ratio(modelparams):
    import numpy as np
    Bta, Btd = modelparams
    Etot, Eta, Etd = MyModel([Bta, Btd], X, gi)
    A = np.mean(Etd)/np.mean(Eta)
    B = gi/(1-gi)
    # The epsilon comes in to loosen a bit only this constraint
    epsilon = 0.1
    return  -abs(abs(A-B)-epsilon)

# This is my solution to make the parameters different from zero.
# The ineq-type constraint makes them >=0.
def TDPos(modelparams):
    Bta, Btd = modelparams
    return Btd - 10**(-5) 
def TAPos(modelparams):
    Bta, Btd = modelparams
    return Bta - 10**(-5)

constraints=[{'type': 'ineq', 'fun': Ratio},
             {'type': 'ineq', 'fun': TDPos},
             {'type': 'ineq', 'fun': TAPos}]

# Bounds or Model Parameters
bounds=((0, None), (0, None))

# Minimize
modelparams0=[Target/np.nanmean(var1), Target/np.nanmean(var2)]
result = opt.minimize(Obj, modelparams0, 
                      tol=0.1,
                      method='SLSQP',
                      options={'maxiter': 40000 }, #,'ftol': 0.1}, 
                      bounds=bounds,
                      constraints=constraints)
print(result)

打印出来：

     fun: 3.0
     jac: array([439.92537314,  77.31019938])
 message: 'Optimization terminated successfully.'
    nfev: 20
     nit: 4
    njev: 4
  status: 0
 success: True
       x: array([0., 0.])

我的问题：fun: 3.0 > tol: 0.1 这是不想要的。

TL;DR： scipy.optimize.minimize 忽略 stop 参数tol。为什么？

编辑：此外，最佳解决方案 [0, 0] 忽略了两个 ineq 约束，旨在使这两个参数> 10**（-5）。这是同一个问题的一部分吗？

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