Python Scipy中的线性编程

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.

Answer 1

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).

Answer 2

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.])