Linear programming in Python scipy

Question

Objective:

maximize :((((alpha1*5000)+(alpha2*0.49431))-5000) + (((alpha1*5000)+(alpha2*0.49431))-0.49431))

constarints:

mod(alpha) <= 1

Code:

from scipy.optimize import minimize
alpha  = [0,0];v1 = 5000
v2 = 0.49431537320810676

def objective(alpha,sign = -1.0):
    alpha1 = alpha[0]
    alpha2 = alpha[1]
    return sign*((((alpha1*5000)+(alpha2*0.49431537320810676))-5000) + (((alpha1*5000)+(alpha2*0.49431537320810676))-0.49431537320810676)) 

def constraint1(alpha):

    return (1- abs (alpha[0]))

def constraint2(alpha):

    return (1- abs (alpha[1]))

con1 = {'type':'ineq','fun':constraint1}
con2 = {'type':'ineq','fun':constraint2}
cons = [con1,con2]

sol = minimize(objective,alpha,method='SLSQP',constraints = cons)

I have given the sign in the objective function to change the optimization to maximize.

Solution:

(sol.x)
 >>>>[ 1.00104909  0.99560862]

I have given the constraints for the alpha for it to be less than 1 , but getting the solutions more than 1.

You are using an NLP solver to solve an LP. That is almost always a bad idea. In addition you use non-differentiable functions abs(x), while this NLP solver assumes smooth functions. This is just a bad approach to solving your problem. — Erwin Kalvelagen
– Erwin Kalvelagen, Commented Jun 29, 2017 at 20:32

Stelios · Accepted Answer · 2017-06-29 16:44:20Z

2

If you see examine the returned object sol, you will see that it has a property .message with the "value"

'Positive directional derivative for linesearch'

which, according to this answer, implies failure to guarantee that the returned solution is optimal. Indeed, it violates the constraints.

This behavior is probably due to the problem having a solution at the boundary of the domain of the optimization variables. Indeed, CVXPY, which is a much better option for linear programming than SLSQP, returns the optimal optimization variable equal to [1,1].

You may want to try scipy.optimize.linprog as a more suitable scipy function for linear programs, although I believe that it is not as fast as CVXPY (or other free LP packages).

answered Jun 29, 2017 at 16:44

Stelios

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Uvar · Accepted Answer · 2017-06-29 16:49:33Z

1

Constraints can be violated and are mainly used for relations between parameters. What you are looking for is the keyword bounds.

from scipy.optimize import minimize
alpha  = [0.,0.];v1 = 5000
v2 = 0.49431537320810676

def objective(alpha,sign = -1.0):
    alpha1 = alpha[0]
    alpha2 = alpha[1]
    return sign*(alpha1*v1+alpha2*v2-v1 + alpha1*v1+alpha2*v2-v2) 

sol = minimize(objective,alpha,method='SLSQP', bounds = ((-1,1),(-1,1)))
sol.x
>> array([ 1.,  1.])

answered Jun 29, 2017 at 16:49

Uvar

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