On 2013-01-29, Daniel Friedan <dfrie...@gmail.com> wrote:
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> 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.
No, they are not. Note that you round the output,
which need not be integer.
If in the last line you do
print 'w_%s = %s' % (i, v)
you get
w_0 = 15/2
w_1 = 5
w_2 = 3/2
w_3 = 1
which is OK.
The original example does integer LP, by the way (and PPL can't so it).
So it's OK to round in this case, but not for an ordinary LP...
Best,
Dmitrii
>
> 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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