用scipy最小化带参数的函数

Question

我想问一下如何用scipy minimize中的优化方法最小化一个函数（误差平方和）。我试过，但似乎我做得不好，因为错误和参数没有改变从初始值。 这是我的密码：

def objective(p, y):
    y = np.array([98.494500, 97.828500, 97.610000, 97.314000, 97.014500, 92.959000, 96.696222])
    p = beta0, beta1, beta2, beta3, tau1, tau2
    return  (((100 * DiscountFactor('rate',np.exp(p[0] + (p[1]+ p[2]) * (1 - np.exp(-yearfractionTenors()/p[4])) * p[4]/yearfractionTenors() - p[2] * np.exp(-yearfractionTenors()/p[4]) + p[3] * (1 - np.exp(-yearfractionTenors()/p[5])) * p[5] / yearfractionTenors() - p[3] * np.exp(-yearfractionTenors() / p[5])) -1, fecha_valoracion, maturity, composition= 'linear', basis= 'act/360').result) - y) ** 2).sum()
x0 = np.array([0.03, -0.03, 0, 0, 1, 1]) #Initial values of beta0, beta1, beta2, beta3, tau1 and tau2
res = optimize.minimize(objective, x0, args = y)
print(res)
output: fun: 64.30571361326217
hess_inv: array([[1, 0, 0, 0, 0, 0],
   [0, 1, 0, 0, 0, 0],
   [0, 0, 1, 0, 0, 0],
   [0, 0, 0, 1, 0, 0],
   [0, 0, 0, 0, 1, 0],
   [0, 0, 0, 0, 0, 1]])
  jac: array([0., 0., 0., 0., 0., 0.])
  message: 'Optimization terminated successfully.'
  nfev: 8
  nit: 0
  njev: 1
 status: 0
 success: True
    x: array([ 0.03, -0.03,  0.  ,  0.  ,  1.  ,  1.  ])

似乎我的错误是我没有很好地使用输入值（初始值）。我想知道是否有人能帮我解决这个问题。 基本上，我想知道如何通过改变初始数组中的参数来最小化函数。也许错误在目标函数中。 这个问题的一个小例子：

def objective(p, y):
    y = np.array([98.494500, 97.828500, 97.610000, 97.314000, 97.014500, 92.959000, 96.696222])
    p = beta0, beta1, beta2, beta3, tau1, tau2
    return  (((100 * DiscountFactor('rate',np.exp(p[0] + (p[1]+ p[2]) * (1 - np.exp(-yearfractionTenors()/p[4])) * p[4]/yearfractionTenors() - p[2] * np.exp(-yearfractionTenors()/p[4]) + p[3] * (1 - np.exp(-yearfractionTenors()/p[5])) * p[5] / yearfractionTenors() - p[3] * np.exp(-yearfractionTenors() / p[5])) -1, fecha_valoracion, maturity, composition= 'linear', basis= 'act/360').result) - y) ** 2).sum()
x0 = np.array([0.03, -0.03, 0, 0, 1, 1]) #Initial values of beta0, beta1, beta2, beta3, tau1 and tau2
res = optimize.minimize(objective, x0, args = y)
print(res)

折扣系数函数是不相关的，但下面是运行它所需的类：

class DiscountFactor:

def __init__(self, val_given, value, start_date, end_date, composition, basis):
    self.start_date = start_date
    self.end_date = end_date
    self.composition = composition
    self.basis = basis
    self.yf = year_fraction(start_date, end_date, basis)

    if val_given == 'rate':
        self.rate_to_df(value) 
    else:
        raise ValueError('val_given must be: rate or df' )

def rate_to_df(self, rate):
    if self.composition == 'linear':
        df = 1/( 1 + rate*self.yf)
    else:
        raise ValueError('composition must be one of the following: linear, yearly, biannual, continuous')
    self.result = df
    return self.result

Answer 1

作为Askold Ilvento，您正在函数范围内重新定义参数。这将使优化失败，因为函数将始终产生相同的结果；这也是一种不好的做法，也是一个潜在的错误源。尝试：

def objective(p, y):
    return  (((100 * DiscountFactor('rate',np.exp(p[0] + (p[1]+ p[2]) * (1 - np.exp(-yearfractionTenors()/p[4])) * p[4]/yearfractionTenors() - p[2] * np.exp(-yearfractionTenors()/p[4]) + p[3] * (1 - np.exp(-yearfractionTenors()/p[5])) * p[5] / yearfractionTenors() - p[3] * np.exp(-yearfractionTenors() / p[5])) -1, fecha_valoracion, maturity, composition= 'linear', basis= 'act/360').result) - y) ** 2).sum()

x0 = np.array([0.03, -0.03, 0, 0, 1, 1]) #Initial values of beta0, beta1, beta2, beta3, tau1 and tau2
y = np.array([98.494500, 97.828500, 97.610000, 97.314000, 97.014500, 92.959000, 96.696222]) 
beta0, beta1, beta2, beta3, tau1, tau2 = optimize.minimize(objective, x0, args = y)