# NLP written by GAMS Convert at 02/17/22 17:19:06
#
# Equation counts
#     Total        E        G        L        N        X        C        B
#         2        0        0        2        0        0        0        0
#
# Variable counts
#                  x        b        i      s1s      s2s       sc       si
#     Total     cont   binary  integer     sos1     sos2    scont     sint
#         6        6        0        0        0        0        0        0
# FX      0
#
# Nonzero counts
#     Total    const       NL
#         8        8        0
#
# Reformulation has removed 1 variable and 1 equation

from pyomo.environ import *

model = m = ConcreteModel()

m.x1 = Var(within=Reals, bounds=(0,1), initialize=0)
m.x2 = Var(within=Reals, bounds=(0,1), initialize=1)
m.x3 = Var(within=Reals, bounds=(0,1), initialize=0)
m.x4 = Var(within=Reals, bounds=(0,1), initialize=1)
m.x5 = Var(within=Reals, bounds=(0,1), initialize=1)
m.x6 = Var(within=Reals, bounds=(0,None), initialize=20)

m.obj = Objective(sense=minimize, expr= -0.5 * (m.x1 * m.x1 + m.x2 * m.x2 +
    m.x3 * m.x3 + m.x4 * m.x4 + m.x5 * m.x5) - 10.5 * m.x1 - 7.5 * m.x2 - 3.5 *
    m.x3 - 2.5 * m.x4 - 1.5 * m.x5 - 10 * m.x6)

m.e1 = Constraint(expr= 6 * m.x1 + 3 * m.x2 + 3 * m.x3 + 2 * m.x4 + m.x5
    <= 6.5)
m.e2 = Constraint(expr= 10 * m.x1 + 10 * m.x3 + m.x6 <= 20)