Want to do multi-variation minimize with sympy

Question

I want to use minimization with scipy.optimize using Symbolized charactors

from scipy.optimize import minimize
from sympy.utilities.lambdify import lambdify
import sympy as sp


x1, x2, x3, x4 = sp.symbols('x1 x2 x3 x4')

FormulaMain = sp.symbols('-2*x1**2*x3+6*x1**2*x4+13*x1**2-3*x1*x2**2+x1*x2+3*x1*x3**2-3*x4+103')
HandleMain  = lambdify((x1,x2,x3,x4),FormulaMain,'numpy')
bnds = ((-1, 1), (-1, 1), (-1, 1), (-1, 1))

PrintParams  = minimize(HandleMain,[1,1,1,1],method='SLSQP',bounds=bnds)

print PrintParams

When I run the code, I get

<lambda>() takes exactly 4 arguments (1 given)

I think I have input 4 argument with [1,1,1,1] Are there anything I have to change with the code?

Answer 1

First of all: Welcome to SO!

As far as I know, lambdify() cannot deal with vectors. Furthermore, when using Sympy, determining the jacobian is easy. You could try:

import numpy as np
from scipy.optimize import minimize
from sympy.utilities.lambdify import lambdify
import sympy as sy

sy.init_printing()  # LaTeX like pretty printing for IPython


x1, x2, x3, x4 = sy.symbols('x1 x2 x3 x4')
xx = (x1, x2, x3, x4)
f = -2*x1**2*x3+6*x1**2*x4+13*x1**2-3*x1*x2**2+x1*x2+3*x1*x3**2-3*x4+103
f_n = lambdify(xx, f, modules='numpy')

# Build Jacobian:
jac_f = [f.diff(x) for x in xx]
jac_fn = [lambdify(xx, jf, modules='numpy') for jf in jac_f]


def f_v(zz):
    """ Helper for receiving vector parameters """
    return f_n(zz[0], zz[1], zz[2], zz[3])


def jac_v(zz):
    """ Jacobian Helper for receiving vector parameters """
    return np.array([jfn(zz[0], zz[1], zz[2], zz[3]) for jfn in jac_fn])


bnds = ((-1, 1), (-1, 1), (-1, 1), (-1, 1))
zz0 = np.array([1, 1, 1, 1])

rslts = minimize(f_v, zz0, method='SLSQP', jac=jac_v, bounds=bnds)
print(rslts)