Dmitrii,
Thanks very much. Sorry for the dumb posting. I should have mentioned
in my posting that I'm just getting into MILP in Sage.
Would it be equally dumb to post a question asking if there is an
arbitrary precision real arithmetic solver for MILP in Sage? (maybe a
version of GLPK?) Google just gives some old pages on the topic.
regards,
Daniel
On 2013-01-29 3:37 PM, Dima Pasechnik wrote:
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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