On 2013-01-29, dfrie...@gmail.com <dfrie...@gmail.com> wrote: > 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. it appears that GLPK has such a functionality (never tried it, nor even read docs :-)); someone has to integrate it in Sage... Should not be too much work, as GLPK is already (mostly) integrated.
There are ways of dealing with low-dimensional ILP problems in Sage, involving enumerating all the integer points in the polytope. MILP is typically hard. If a normal precision MILP never produces an answer, typically arbirary precision won't help, either. Only for some really "bad" data an arbitrary precision MILP would be useful, although I actually saw such data working on bounds of quantum codes recently. Best, Dmitrii > > regards, > Daniel > > On 2013-01-29 3:37 PM, Dima Pasechnik wrote: >> On 2013-01-29, Daniel Friedan <dfrie...@gmail.com> wrote: >>> ------=_Part_964_12292304.1359472365223 >>> Content-Type: text/plain; charset=ISO-8859-1 >>> >>> 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 >>> >>> >> > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
