from gekko import GEKKO
m = GEKKO() # create GEKKO model
# create binary variables
x1 = m.Var(integer=True,lb=0,ub=1) 
x2 = m.Var(integer=True,lb=0,ub=1)
m.Minimize(4*x1**2-4*x2*x1**2+x2**2+x1**2-x1+1)
m.options.SOLVER = 1 # APOPT solver
m.solve()
print('x1: ' + str(x1.value[0]))
print('x2: ' + str(x2.value[0]))