Optimization with constrain

Question

I would like to solve a constrained optimization problem.

max {ln (c1) + ln (c2)}

s.t. 4(c1) + 6(c2) ≤ 40

I wrote this code:

import numpy as np
from scipy import optimize

def main():
    """
    solving a regular constrained optimization problem    
    max ln(cons[0]) + ln(cons[1]) 
    st. prices[0]*cons[0] + prices[1]*cons[1] <= I         
    """    
   
    prices = np.array([4.0, 6.0])
    I = 40.0
   
    util = lambda cons: np.dot( np.log(cons))  #define utility function
    budget = lambda cons: I - np.dot(prices, cons)   #define the budget constraint
    
    initval = 40.0*np.ones(2)    #set the initial guess for the algorithm
    
    res = optimize.minimize(lambda x: -util(x), initval, method='slsqp', 
                            constraints={'type':'ineq', 'fun':budget}, 
                            tol=1e-9)
    assert res['success'] == True
           
    
    print(res)

Unfortunately, my code don't print any solution. Can you help me figure out why?

Answer 1

Your code yields a TypeError since np.dot expects two arguments, see the definition of your utils function. Hence, use

# is the same as np.dot(np.ones(2), np.log(cons))
utils = lambda cons: np.sum(np.log(cons))

instead.