Specifying greater than inequality in scipy
I solved a simple LP problem where all the constraints are "less than or equal".
I used scipy.optimize.linprog for these.
The problem is that one or more equations of the constraints are "greater than or equal". How to indicate this? I need to use the two phase approach provided by scipy.optimize.linprog
An example of this is:
7X1 + 4X2 + 9X3 ≥ 750
4X1 + 6X2 + 7X3 ≤ 40
17X1 + 9X2 + 2.5X3 ≥ 3540
56X1 + 3X2 + 27X3 ≤ 6450
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Here is a wrapper that includes the bottom line lines in the lingprog wording. Note that more error capture is required (for example, the number of columns of each matrix A
must be equal), this should not be a robust implementation. For proper error capture, I suggest you skip the linprog source code .
from scipy.optimize import linprog
import numpy as np
def linprog_lb_wrapper(c, A_ub=None, b_ub=None, A_lb=None, b_lb=None, A_eq=None, b_eq=None, \
bounds=None, method='simplex', callback=None, options=None):
if A_lb is None:
res = linprog(c, A_ub, b_ub, A_eq, b_eq, bounds, method, callback, options)
return res
elif (b_lb is None) or (len(b_lb) != len(A_lb)):
# catch the error here
print('Error')
A_ub_new, b_ub_new = np.array(A_ub), np.array(b_ub)
A_lb_new, b_lb_new = np.array(A_lb), np.array(b_lb)
A_lb_new *= -1.
b_lb_new *= -1.
A_ub_new = np.vstack((A_ub_new, A_lb_new))
b_ub_new = np.vstack((b_ub_new, b_lb_new))
res = linprog(c=c, A_ub=A_ub_new, b_ub=b_ub_new, A_eq=A_eq, b_eq=b_eq, bounds=bounds, \
method=method, callback=callback, options=options)
return res
def test():
c = [0, 0, 0]
A_ub = [[4, 6, 7], [56, 3, 27]]
b_ub = [40, 6450]
A_lb = [[7, 4, 9], [17, 9, 2.5]]
b_lb = [750, 3540]
bounds = ((None, None), (None, None), (None, None))
res = linprog_lb_wrapper(c=c, A_ub=A_ub, b_ub=b_ub, A_lb=A_lb, b_lb=b_lb, bounds=bounds)
print(res)
test()
Note that there is no valid solution for the instance you presented (I also tested this with a different solver and got a proof of not feasibility).
Hope this helps.
This code can be tested here .
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To express a "greater than or equal" constraint in scipy.optimize.linprog , you can multiply each side of the constraint by -1 to convert the constraint to the expected "less than or equal" format.
For example, in the example presented, the constraint matrix with mixed inequalities would be
A = [[7, 4, 9], [4, 6, 7], [17, 9, 2.5], [56, 3, 27]]
with the right side
b = [750, 40, 3540, 6450]
and we want to express constraints as Ax <= b . So, to reverse the necessary inequalities, the constraint matrix becomes
A = [[-7, -4, -9], [4, 6, 7], [-17, -9, -2.5], [56, 3, 27]]
and the right side becomes
b = [-750, 40, -3540, 6450]
Then we can pass the arguments A_ub = A and b_ub = b to linprog .
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