from gekko import GEKKO
import numpy as np
m = GEKKO(remote=False)
x = m.Array(m.Var,4,value=1,lb=1,ub=5)
x1,x2,x3,x4 = x
#change initial values
x2.value = 5; x3.value = 5
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 solution
print('Objective: ',m.options.OBJFCNVAL)
print('Solution: ', x)