The following example from Sage Reference v5.6 >> Numerical Optimization >>
Mixed integer linear programming
http://www.sagemath.org/doc/reference/sage/numerical/mip.html
gives a wrong answer when solver = 'PPL' is used. The equality constraints
are violated.
Sage 5.6-OSX-64bit-10.6 under OS X 10.6.8
sage: p = MixedIntegerLinearProgram(maximization=False, solver = "PPL")
sage: print p.base_ring()
sage: w = p.new_variable()
sage: p.add_constraint(w[0] + w[1] + w[2] - 14*w[3] == 0)
sage: p.add_constraint(w[1] + 2*w[2] - 8*w[3] == 0)
sage: p.add_constraint(2*w[2] - 3*w[3] == 0)
sage: p.add_constraint(w[0] - w[1] - w[2] >= 0)
sage: p.add_constraint(w[3] >= 1)
sage: _ = [ p.set_min(w[i], None) for i in range(1,4) ]
sage: p.set_objective(w[3])
sage: p.show()
sage: print 'Objective Value:', p.solve()
sage: for i, v in p.get_values(w).iteritems():\
sage: print 'w_%s = %s' % (i, int(round(v)))
Rational Field
Minimization:
x_3
Constraints:
constraint_0: 0 <= x_0 + x_1 + x_2 - 14 x_3 <= 0
constraint_1: 0 <= x_1 + 2 x_2 - 8 x_3 <= 0
constraint_2: 0 <= 2 x_2 - 3 x_3 <= 0
constraint_3: - x_0 + x_1 + x_2 <= 0
constraint_4: - x_3 <= -1
Variables:
x_0 is a continuous variable (min=0, max=+oo)
x_1 is a continuous variable (min=-oo, max=+oo)
x_2 is a continuous variable (min=-oo, max=+oo)
x_3 is a continuous variable (min=-oo, max=+oo)
Objective Value: 1
w_0 = 8
w_1 = 5
w_2 = 2
w_3 = 1
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