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pythonconstraintsboundsscipy-optimize-minimize
dpp1992
dpp1992

Reputation: 1

Python - minimize with x[0] < x[1] < x[2] constraint

I am trying to create a minimization program to find the lowest sum squared errors between a predicted value (r) and actual value (x). I am fitting b_1, b_2 and b_3 to obtain r. I am using the minimize function from scipy.optimize(). I have included bounds for each of the 3 variables which works. I also want to include a constraint where b_1<b_2<b_3. However I tried implementing this and received errors: TypeError: numpy boolean subtract, the - operator, is not supported, use the bitwise_xor, the ^ operator, or the logical_xor function instead. Any help would be great!

import numpy as np
import pandas as pd
import sys
import math
import numpy as np
from scipy.optimize import curve_fit
import os
from scipy.optimize import minimize

def psd_fun(c_s):
    b_1 = c_s[0]
    b_2 = c_s[1]
    b_3 = c_s[2]
    a = np.arange(-1.0, 1.01, 0.10)
    b = np.linspace(-1.0, 5.0, 40)
    c = []
    x=282.335
    p_1 = 0.109
    p_2 = 0.102
    p_3 = 0.789
    pt = 0.440

    d1=[]
    d2=[]
    d3=[]
    d12=[]
    d22=[]
    d32=[]
    for i in b:
        z=10**i
        c += [z]
    for i in c:
        d1 += [p_1*(1-math.exp(-(i/b_1)))*pt]
        d2 += [p_2 * (1 - math.exp(-(i / b_2))) * pt]
        d3 += [p_3 * (1 - math.exp(-(i / b_3))) * pt]

    for i in range(1,len(d3),1):
        d12 += [((d1[i]-d1[i-1])/(p_1*pt)*c[i])]
        d22 +=[(d2[i]-d2[i-1])/(p_2*pt)*c[i]]
        d32 +=[(d3[i]-d3[i-1])/(p_3*pt)*c[i]]

    r = sum(d12)*p_1*pt+sum(d22)*p_2*pt+sum(d32)*p_3*pt
    r1 = (r-x)**2
    return r1

cons = ({'type': 'ineq', 'fun': lambda c_s:  np.array([c_s[0] <= c_s[1]])},
        {'type': 'ineq', 'fun': lambda c_s: np.array([c_s[1] <= c_s[2]])})

bnds = ((0.1, 2.5), (15, 500), (400, 10000))
min_res = minimize(psd_fun, [2.5,276,435], bounds = bnds, constraints=cons)
print(min_res)

without using the constraints I obtain:

fun: 3.3969585845074804e-15
 hess_inv: <3x3 LbfgsInvHessProduct with dtype=float64>
      jac: array([6.68100889e-09, 6.30719417e-09, 5.02965289e-08])
  message: 'CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL'
     nfev: 16
      nit: 3
     njev: 4
   status: 0
  success: True
        x: array([  2.5       , 302.27943845, 638.28639494])

Which is fine and what I wanted. However I have some datapoints where the program is not fitting to specifications: b_1<b_2<b_3

Upvotes: 0

Views: 129

Answers (1)

Beano
Beano

Reputation: 7831

I believe that the contraint option can only be used for certain methods (see https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html)

Constraints definition. Only for COBYLA, SLSQP and trust-constr.

Upvotes: 2

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