CODEWITHSUNDEEP
pythonscipy
MLhacker
MLhacker

Reputation: 1512

Using Scipy to minimize variables given inequality conditions of other variables

as an experiment, I'd like to minimize the following objective function:

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The parameters w1 and w2 are bounded by the lambdas:

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The constraints are the following:

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I haven't found a decent Scipy example on how to optimize a multivariate case such as this. If someone could lend a guidance on this problem, I appreciate it.

Upvotes: 2

Views: 1328

Answers (1)

sascha
sascha

Reputation: 33532

Code:

import numpy as np
from scipy.optimize import minimize

def fun(x):
  return np.sum(x[2:])

x0 = np.zeros(4)  # lambda1, lambda 2, w1, w2
cons = ({'type': 'ineq', 'fun': lambda x:  x[2] - 2 + 10 * x[0] + 3 * x[1]},
        {'type': 'ineq', 'fun': lambda x:  x[3] - 2 + 5 * x[0] + 5 * x[1]},
        {'type': 'ineq', 'fun': lambda x:  x[2]},
        {'type': 'ineq', 'fun': lambda x:  x[3]},
        {'type': 'eq', 'fun': lambda x:  x[0] + x[1] - 1})
res = minimize(fun, x0, constraints=cons)
print(res)
print(np.round(res.x, 2))

Output:

fun: -3.3306690738754696e-16
jac: array([ 0.,  0.,  1.,  1.])
message: 'Optimization terminated successfully.'
nfev: 7
nit: 1
njev: 1
status: 0
success: True
  x: array([  5.00000000e-01,   5.00000000e-01,  -3.33066907e-16,
    0.00000000e+00])
[ 0.5  0.5 -0.   0. ]

This is basically only using information from the official docs.

Edit I used the general optimization functions here, but you probably should use scipy.optimize.linprog as this is an LP!

I did not check it, but linprog-usage looks somewhat like:

from scipy.optimize import linprog
c = [0, 0, 1, 1]
A = [[-10, -3, -1, 0], [-5, -5, 0, -1]]
b = [-2, -2]
A_eq = [[1, 1, 0, 0]]
b_eq = [1]
x0_bnds = (-np.inf, -np.inf, 0, 0)
x1_bnds = (np.inf, np.inf, np.inf, np.inf)
res = linprog(c, A, b, A_eq, b_eq, bounds=list(zip(x0_bnds, x1_bnds)))
print(res)

Output:

 fun: -0.0
 message: 'Optimization terminated successfully.'
 nit: 4
 slack: array([ 0.,  3.])
 status: 0
 success: True
   x: array([-0.14285714,  1.14285714,  0.        ,  0.        ])

Upvotes: 3

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