# NLP written by GAMS Convert at 02/17/22 17:19:10
#
# Equation counts
#     Total        E        G        L        N        X        C        B
#         4        4        0        0        0        0        0        0
#
# Variable counts
#                  x        b        i      s1s      s2s       sc       si
#     Total     cont   binary  integer     sos1     sos2    scont     sint
#         5        5        0        0        0        0        0        0
# FX      0
#
# Nonzero counts
#     Total    const       NL
#        11        6        5
#
# Reformulation has removed 1 variable and 1 equation

from pyomo.environ import *

model = m = ConcreteModel()

m.x1 = Var(within=Reals, bounds=(None,None), initialize=0.5)
m.x2 = Var(within=Reals, bounds=(None,None), initialize=0.5)
m.x3 = Var(within=Reals, bounds=(None,None), initialize=2)
m.x4 = Var(within=Reals, bounds=(None,None), initialize=1)
m.x5 = Var(within=Reals, bounds=(None,None), initialize=1)

m.obj = Objective(sense=minimize, expr= m.x1 * log(m.x1) + m.x2 * log(m.x2) -
    log(m.x3 - m.x5) + m.x3 - 0.353553390593274 * log((m.x3 + 2.41421356237309
    * m.x5) / (m.x3 - 0.414213562373095 * m.x5)) * m.x4 / m.x5 +
    2.5746329124341 * m.x1 + 0.54639755131421 * m.x2 - 1)

m.e1 = Constraint(expr= m.x3**3 - m.x3**2 * (1 - m.x5) + m.x3 * (-3 * m.x5**2
    - 2 * m.x5 + m.x4) - m.x4 * m.x5 + m.x5**3 + m.x5**2 == 0)
m.e2 = Constraint(expr= -0.884831 * m.x1 * m.x1 - 0.555442 * m.x1 * m.x2 -
    0.555442 * m.x2 * m.x1 - 0.427888 * m.x2 * m.x2 + m.x4 == 0)
m.e3 = Constraint(expr= -0.0885973 * m.x1 - 0.0890893 * m.x2 + m.x5 == 0)
m.e4 = Constraint(expr= m.x1 + m.x2 == 1)