scipy.optimize.linprog unable to find a feasible starting point despite a feasible answer clearly exists

Question

the vector k seems to satisfy all constraints. Is there something I\'m missing here? Thanks.

import numpy as np
from scipy.optimize import linprog
A_ub=[[0,          


        

Answer 1

This answer doesn't explain why it works. I hope someone more familiar with the linprog code or with linear programming in general can give a more thorough answer.

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I get a solution if I use the option bland=True (see show_options for documentation--scroll to the bottom for the linprog options):

In [130]: linprog(c, A_ub, b_ub, A_eq, b_eq, options=dict(bland=True))
Out[130]: 
  status: 0
   slack: array([  3610.,   6490.,  11840.,      0.,      0.,  14000.,  10100.,
            0.,  10000.,   5000.,  15450.,      0.,  13000.,      0.,
        10000.,   3000.,  11000.,      0.,  12220.,      0.,  10000.])
 success: True
     fun: -2683.6935269049131
       x: array([  1.22573363e+00,   2.00000000e+00,   1.22404780e+00,
         3.71739130e+00,   8.25688073e-02,   2.00000000e+03,
         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
         5.00000000e+03,   0.00000000e+00,   0.00000000e+00,
         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
         0.00000000e+00,   0.00000000e+00,   2.00000000e+03,
         6.39000000e+03,   0.00000000e+00,   0.00000000e+00,
         0.00000000e+00,   0.00000000e+00,   1.84000000e+03,
         5.00000000e+03,   0.00000000e+00,   1.00000000e+04,
         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
         0.00000000e+00,   1.00000000e+02,   0.00000000e+00,
         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
         0.00000000e+00,  -1.11022302e-12,   0.00000000e+00,
         5.45000000e+03,   0.00000000e+00,   3.00000000e+03,
         0.00000000e+00,   3.00000000e+03,   0.00000000e+00,
         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
         1.00000000e+03])
 message: 'Optimization terminated successfully.'
     nit: 50

One component is slightly negative (-1.11e-12). Presumably this is within the default tolerance. That can be cleaned up by lowering the tolerance (but note the change in x[19]):

In [131]: linprog(c, A_ub, b_ub, A_eq, b_eq, options=dict(bland=True, tol=1e-15))
Out[131]: 
  status: 0
   slack: array([  3610.,   6490.,  11840.,      0.,      0.,  14000.,  10100.,
            0.,  10000.,   5000.,  15450.,      0.,  13000.,      0.,
        10000.,   3000.,  11000.,      0.,  12220.,      0.,  10000.])
 success: True
     fun: -2683.693526904935
       x: array([  1.22573363e+00,   2.00000000e+00,   0.00000000e+00,
         3.71739130e+00,   8.25688073e-02,   2.00000000e+03,
         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
         5.00000000e+03,   0.00000000e+00,   0.00000000e+00,
         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
         0.00000000e+00,   1.63900000e+04,   0.00000000e+00,
         0.00000000e+00,   0.00000000e+00,   2.00000000e+03,
         6.39000000e+03,   0.00000000e+00,   0.00000000e+00,
         0.00000000e+00,   0.00000000e+00,   1.84000000e+03,
         5.00000000e+03,   0.00000000e+00,   1.00000000e+04,
         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
         0.00000000e+00,   1.00000000e+02,   0.00000000e+00,
         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
         5.45000000e+03,   0.00000000e+00,   3.00000000e+03,
         0.00000000e+00,   3.00000000e+03,   0.00000000e+00,
         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
         0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
         1.00000000e+03])
 message: 'Optimization terminated successfully.'
     nit: 51