[Couenne] Problem Reformulation (P) and (P')

Thu Jul 9 12:50:04 EDT 2009

Dear Pietro,

      The response is adequate. Just one important thing. Why the variables
values are so different ? (See the attached file).

      in other words, what to do for getting variables values differences
more closest ? at least less than 1e-5.

Regards,

Sismail

2009/6/30 Pietro Belotti <belotti at lehigh.edu>
Dear Sismail,

I'm attaching below the output of Couenne on both instances. The optimal
solution is zero, and the two "different" numbers obtained are both very
close to zero -- they are indeed returned by Ipopt, the NLP solver used by
Couenne. In this case I wouldn't say the two solutions are different.

Also, testb.mod is reformulated by Couenne so that the first variables to
appear in the AMPL file, testb.mod, i.e., x[6], x[7], and x[8], are indeed
the first variables in the model file loaded by Couenne. This is again a
slight difference in the model, but only related to a re-numbering of the
variables.

Hope this helps.

Best,
Pietro

[pbelotti ~] couenne testa

objectives:
min ((-0.1+(x_0+x_1+x_2+(2*x_3)+(
>
> 2*x_4)+(2*x_5)))^2)
> constraints:
> variables:
> x_0 [ 0 , 1 ]
> x_1 [ 0 , 1 ]
> x_2 [ 0 , 1 ]
> x_3 [ 0 , 1 ]
> x_4 [ 0 , 1 ]
> x_5 [ 0 , 1 ]
> end
> Problem size before reformulation: 6 variables (0 integer), 0 constraints.
> Problem size after  reformulation: 8 variables (0 integer), 0 constraints.
>
> NLP0012I
>              Num      Status      Obj             It       time
> NLP0013I     1        OPT         7.24915497916231e-16    8        0.008001
> Cbc0012I Integer solution of 7.24915e-16 found by Init Rounding NLP after 0
> iterations and 0 nodes (0.00 seconds)
> NLP0013I     2        OPT         1.230414883748645e-20   3        0.004
> Cbc0001I Search completed - best objective 7.24915497916231e-16, took 0
> iterations and 0 nodes (0.00 seconds)
> Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost
>
> couenne Optimal
>
>        "Finished"
>
>
> [pbelotti ~] couenne testb
>
> objectives:
> min ((-0.1+(x_0+x_1+x_2))^2)
> constraints:
> ( +1*x_8 +1*x_7 +1*x_3 -1*x_0) = 0
> ( +1*x_8 +1*x_6 +1*x_4 -1*x_1) = 0
> ( +1*x_7 +1*x_6 +1*x_5 -1*x_2) = 0
> variables:
> x_0 [ 0 , 3 ]
> x_1 [ 0 , 3 ]
> x_2 [ 0 , 3 ]
> x_3 [ 0 , 1 ]
> x_4 [ 0 , 1 ]
> x_5 [ 0 , 1 ]
> x_6 [ 0 , 1 ]
> x_7 [ 0 , 1 ]
> x_8 [ 0 , 1 ]
> end
> Problem size before reformulation: 9 variables (0 integer), 3 constraints.
> Problem size after  reformulation: 11 variables (0 integer), 0 constraints.
>
>
> ******************************************************************************
> This program contains Ipopt, a library for large-scale nonlinear
> optimization.
>  Ipopt is released as open source code under the Common Public License
> (CPL).
>         For more information visit http://projects.coin-or.org/Ipopt
>
> ******************************************************************************
>
> NLP0012I
>              Num      Status      Obj             It       time
> NLP0013I     1        OPT         8.626481252066872e-18   4        0.004
> Cbc0012I Integer solution of 8.62648e-18 found by Init Rounding NLP after 0
> iterations and 0 nodes (0.00 seconds)
> NLP0013I     2        OPT         2.593450360578931e-25   4        0.004
> Cbc0001I Search completed - best objective 8.626481252066872e-18, took 0
> iterations and 0 nodes (0.00 seconds)
> Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost
>
> couenne Optimal
>
>        "Finished"
>
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bonmin: 
ANALYSIS TEST: objectives:
min ((-0.1+(x_0+x_1+x_2+(2*x_3)+(2*x_4)+(2*x_5)))^2)
constraints:
variables:
x_0 [ 0 , 1 ]
x_1 [ 0 , 1 ]
x_2 [ 0 , 1 ]
x_3 [ 0 , 1 ]
x_4 [ 0 , 1 ]
x_5 [ 0 , 1 ]
end
Problem size before reformulation: 6 variables (0 integer), 0 constraints.
Problem size after  reformulation: 8 variables (0 integer), 0 constraints.

******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
 Ipopt is released as open source code under the Common Public License (CPL).
         For more information visit http://projects.coin-or.org/Ipopt
******************************************************************************

NLP0012I 
              Num      Status      Obj             It       time
NLP0013I     1        OPT         8.697067777597651e-20   4        0.01
Cbc0012I Integer solution of 8.69707e-20 found by Init Rounding NLP after 0 iterations and 0 nodes (-0.00 seconds)
NLP0013I     2        OPT         2.040481338814703e-17   4        0.01
Clp0000I Optimal - objective value 0
Clp0000I Optimal - objective value 0
Cbc0001I Search completed - best objective 8.697067572964179e-20, took 0 iterations and 0 nodes (0.02 seconds)
Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost
 	"Finished"
x [*] :=
0  0.0107251
1  0.0107251
2  0.0107251
3  0.0113041
4  0.0113041
5  0.0113041
;

bonmin: 
ANALYSIS TEST: objectives:
min ((-0.1+(x_0+x_1+x_2))^2)
constraints:
( +1*x_8 +1*x_7 +1*x_3 -1*x_0) = -0
( +1*x_8 +1*x_6 +1*x_4 -1*x_1) = -0
( +1*x_7 +1*x_6 +1*x_5 -1*x_2) = -0
variables:
x_0 [ 0 , 3 ]
x_1 [ 0 , 3 ]
x_2 [ 0 , 3 ]
x_3 [ 0 , 1 ]
x_4 [ 0 , 1 ]
x_5 [ 0 , 1 ]
x_6 [ 0 , 1 ]
x_7 [ 0 , 1 ]
x_8 [ 0 , 1 ]
end
Problem size before reformulation: 9 variables (0 integer), 3 constraints.
Problem size after  reformulation: 11 variables (0 integer), 0 constraints.

******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
 Ipopt is released as open source code under the Common Public License (CPL).
         For more information visit http://projects.coin-or.org/Ipopt
******************************************************************************

NLP0012I 
              Num      Status      Obj             It       time
NLP0013I     1        OPT         4.846098492936827e-14   5        0.02
Cbc0012I Integer solution of 4.8461e-14 found by Init Rounding NLP after 0 iterations and 0 nodes (0.00 seconds)
NLP0013I     2        OPT         7.796019770154386e-20   4        0.01
Clp0000I Optimal - objective value 0
Clp0000I Optimal - objective value 0
Cbc0001I Search completed - best objective 4.846098492936827e-14, took 0 iterations and 0 nodes (0.01 seconds)
Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost
 	"Finished"
x [*] :=
0  0.0168945
1  0.0168945
2  0.0168945
3  0.00821944
4  0.00821944
5  0.00821944
6  0.0333334
7  0.0333334
8  0.0333334
;