Using scipy optimize minimize does not minimize function

Question

im new into Python and i try to figure out how everythings work. I have a little problem with the minimize function of the scipy.optimize package. I try to minimize a given function with some start values but python gives me very high parameter values. This ist my simple code:

import numpy as np
from scipy.optimize import minimize
global array
y_wert = np.array([1,2,3,4,5,6,7,8])
global x_wert
x_wert = np.array([1,2,3,4,5,6,7,8])
def Test(x):
    Summe = 0
    for i in range(0,len(y_wert)):
        Summe = Summe + (y_wert[i] - (x[0]*x_wert[i]+x[1]))
    return(Summe)
x_0 = [1,0]
xopt = minimize(Test,x_0, method='nelder-mead',options={'xatol': 1e-8, 'disp': True})
print(xopt)

If i run this script the best given parameters are:

[1.02325529e+44, 9.52347084e+40]

which really doesnt solve this problem. Ive also try some slightly different startvalues but that doesnt solve my problems. Can anyone give me a clue as to where my mistake lies? Thanks a lot for your help!

You want to minimize the absolute value of the sum. Your code minimizes a negative sum to -∞. In Test do: return(abs(Summe)). Also have a look at the output message, it is usually very valuable information. The success field needs checking before interpreting the results. — Jacques Gaudin
– Jacques Gaudin, Commented Mar 11, 2020 at 0:41

Alistair · Accepted Answer · 2020-03-11 00:44:54Z

1

Your test function is effectively a straight line with negative gradient so there is no minimum, it's an infinitely decreasing function, that explains your large results, try something like x squared instead

answered Mar 11, 2020 at 0:44

Alistair

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JeeyCi · Accepted Answer · 2024-09-02 10:52:21Z

im new into Python and i try to figure out how everythings work. I have a little problem with the minimize function of the scipy.optimize package. I try to minimize a given function with some start values

you can minimize SSE loss-function as for Ordinary_Least_Squares fitting any model curve:

# # This does not give you the parameter errors though ... you'd have
# to estimate the HESSE matrix separately ...
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.optimize import minimize

#######################################
## Nelson_Siegel_Svensson_model
β0 = 0.01
β1 = 0.01
β2 = 0.01
β3 = 0.01
λ0 = 1.00
λ1 = 1.00

TimeVec = np.array([1,2,5,10,25])
YieldVec = np.array([0.0039, 0.0061, 0.0166, 0.0258, 0.0332])

def model(T, c):
    n= (c[0])+(c[1]*((1-np.exp(-T/c[4]))/(T/c[4])))+(c[2]*((((1-np.exp(-T/c[4]))/(T/c[4])))-(np.exp(-T/c[4]))))+(c[3]*((((1-np.exp(-T/c[5]))/(T/c[5])))-(np.exp(-T/c[5]))))

    return n

def loss(params,  TimeVec, YieldVec):
    sse= np.sum((model(TimeVec, params)-YieldVec)**2)
    return sse

c = minimize(loss, np.array([β0, β1, β2, β3, λ0, λ1]),  args = (TimeVec, YieldVec), method="BFGS" , tol= 1.4e-20).x

plt.scatter(TimeVec , YieldVec)
plt.plot(TimeVec , model(TimeVec, c) )
plt.xlabel('Period')
plt.ylabel('Interest (YTD)')
plt.title("Nelson-Siegel-Svensson Model - Fitted Yield Curve", fontsize= 10)
import matplotlib.ticker as mtick
plt.gca().yaxis.set_major_formatter(mtick.PercentFormatter(1))
##ax.yaxis.set_major_formatter(mtick.PercentFormatter())
plt.tight_layout()
plt.show()

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