Python constrained non-linear optimization

Question

What\'s the recommended package for constrained non-linear optimization in python ?

The specific problem I\'m trying to solve is this:

I have an unknown

Answer 1

As others have commented as well, the SciPy minimize package is a good place to start. We also have a review of many other optimization packages in the Python Gekko paper (see Section 4). I've included an example below (Hock Schittkowski #71 benchmark) that includes an objective function, equality constraint, and inequality constraint in Scipy.optimize.minimize.

import numpy as np
from scipy.optimize import minimize

def objective(x):
    return x[0]*x[3]*(x[0]+x[1]+x[2])+x[2]

def constraint1(x):
    return x[0]*x[1]*x[2]*x[3]-25.0

def constraint2(x):
    sum_eq = 40.0
    for i in range(4):
        sum_eq = sum_eq - x[i]**2
    return sum_eq

# initial guesses
n = 4
x0 = np.zeros(n)
x0[0] = 1.0
x0[1] = 5.0
x0[2] = 5.0
x0[3] = 1.0

# show initial objective
print('Initial SSE Objective: ' + str(objective(x0)))

# optimize
b = (1.0,5.0)
bnds = (b, b, b, b)
con1 = {'type': 'ineq', 'fun': constraint1} 
con2 = {'type': 'eq', 'fun': constraint2}
cons = ([con1,con2])
solution = minimize(objective,x0,method='SLSQP',\
                    bounds=bnds,constraints=cons)
x = solution.x

# show final objective
print('Final SSE Objective: ' + str(objective(x)))

# print solution
print('Solution')
print('x1 = ' + str(x[0]))
print('x2 = ' + str(x[1]))
print('x3 = ' + str(x[2]))
print('x4 = ' + str(x[3]))

Here is the same problem with Python Gekko:

from gekko import GEKKO
m = GEKKO()
x1,x2,x3,x4 = m.Array(m.Var,4,lb=1,ub=5)
x1.value = 1; x2.value = 5; x3.value = 5; x4.value = 1

m.Equation(x1*x2*x3*x4>=25)
m.Equation(x1**2+x2**2+x3**2+x4**2==40)
m.Minimize(x1*x4*(x1+x2+x3)+x3)

m.solve(disp=False)
print(x1.value,x2.value,x3.value,x4.value)

There is also a more comprehensive discussion thread on nonlinear programming solvers for Python if SLSQP can't solve your problem. My course material on Engineering Design Optimization is available if you need additional information on the solver methods.