On 2013-01-31, Daniel Friedan <[email protected]> wrote: > ------=_Part_880_30796308.1359641848689 > Content-Type: text/plain; charset=ISO-8859-1 > > First, I'll try my MILP problems in double-precision (probably using > CPLEX). I'll re-post my question about arbitrary precision if it turns out > that I need it. IMHO the main problem with MILPs is that it's pretty hard to get a certificate of optimality (much easier with LPs/SDPs). Commercial solvers don't do them, free solvers don't do them either, AFAIK. (that's OK if you just want to use the solution obtained, but claiming anything about optimality is a different matter) > > We definitely needed arbitrary precision when we did some related problems > using semi-definite programming (over the real numbers -- without the > integrality constraints). To use arbitrary precision floating point > arithmetic, we had to employ SDPA-GMP as our SDP-solver, invoking it from > Sage via a shell script.
SDPs are known to be much more demanding in this sense, and for good geometric/algebraic reasons too. Best, Dmitrii > > Thanks again for the help. > > Daniel > > On Tuesday, January 29, 2013 3:12:45 PM UTC, Daniel Friedan wrote: >> >> 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 >> >> >> > -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
