SLSQP constrained minimization error in 1.5.2

SLSQP minimization fails to correctly solve a constrained minimization problem in v1.5.2, which it is able to solve in v1.1.0.

Sample code with the problem explanation, followed by outputs with the two scipy versions

Code

#
# find (Nx1) w that minimizes w'Qw, subject to:
#  - non-negative elements in w
#  - third element of w = 0.2
#  - elements of w sum to one
#  - w'r = 0.05862
# correct answer is w = [0, 0, 0.2, 0, 0.8]

import numpy as np
import scipy as sc
from scipy.optimize import minimize
from scipy.optimize import Bounds

Q = np.array([[0.00463, 0.00407, 0.00102, 0.00212, 0.00272],
              [0.00407, 0.00412, 0.00079, 0.00185, 0.00289],
              [0.00102, 0.00079, 0.00039, 0.00061, 0.00054],
              [0.00212, 0.00185, 0.00061, 0.00134, 0.00129],
              [0.00272, 0.00289, 0.00054, 0.00129, 0.00214]])
r = np.array([0.12964, 0.11086, 0.03439, 0.11594, 0.06468])
wInit = np.ones((5,1)) * 0.2

bounds = Bounds([0,0,0.2,0,0],
                [1,1,0.2,1,1])
objective = lambda w: np.sqrt(w.dot(Q).dot(w.T))
constraints = ({'type': 'eq', 'fun': lambda w: w.sum() - 1},
                {'type': 'eq', 'fun': lambda w: w.dot(r.T) - 0.05862})  

res = minimize(objective, wInit, method='SLSQP', bounds=bounds, 
                           constraints=constraints)`

print ("Scipy version " + sc.__version__)
print ("Condition number of Q is %.1f" % np.linalg.cond(Q))
print (res)

Output with v1.1.0

Scipy version 1.1.0
Condition number of Q is 373.2
     fun: 0.039471508711981115
     jac: array([0.0603 , 0.06258, 0.01292, 0.02924, 0.04611])
 message: 'Optimization terminated successfully.'
    nfev: 300
     nit: 23
    njev: 19
  status: 0
 success: True
       x: array([3.34781e-17, 1.54010e-16, 2.00000e-01, 9.75493e-17, 8.00000e-01])

Output with v1.5.2

Scipy version 1.5.2
Condition number of Q is 373.2
     fun: 0.0440090899701414
     jac: array([0.06616815, 0.06235076,        nan, 0.03276596, 0.04353646])
 message: 'Inequality constraints incompatible'
    nfev: 6
     nit: 1
    njev: 1
  status: 4
 success: False
       x: array([0.2, 0.2, 0.2, 0.2, 0.2])
C:\ProgramData\Anaconda3\lib\site-packages\scipy\optimize\_numdiff.py:519: RuntimeWarning: invalid value encountered in true_divide
  J_transposed[i] = df / dx

[andyfaff]

I think this is a duplicate of issue #12502, and would be fixed by PR #12889 (with a better description in #12539). The main issue here is that the numerical differentiation now strictly obeys bounds, and it cannot deal with an upper bound that is equal to a lower bound. The proposed fix identifies those parameter entries and sets the gradient to 0 for that entry. With #12502 applied the output for your example comes to:

     fun: 0.0394715087119811
     jac: array([0.06029666, 0.06257678, 0.        , 0.02923628, 0.04610921])
 message: 'Positive directional derivative for linesearch'
    nfev: 10
     nit: 6
    njev: 2
  status: 8
 success: False
       x: array([0. , 0. , 0.2, 0. , 0.8])

[andyfaff]

Should be fixed with #13096