Dear Pietro,<br><br> The response is adequate. Just one important thing. Why the variables values are so different ? (See the attached file).<br><br> in other words, what to do for getting variables values differences more closest ? at least less than 1e-5.<br>
<br>Regards,<br><br>Sismail<br><br><br>2009/6/30 Pietro Belotti <span dir="ltr"><<a href="mailto:belotti@lehigh.edu">belotti@lehigh.edu</a>></span><br>Dear Sismail,<br>
<br>
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.<br>
<br>
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.<br>
<br>
Hope this helps.<br>
<br>
Best,<br>
Pietro<br>
<br>
<br>
[pbelotti ~] couenne testa<br>
<br>
objectives:<br>
min ((-0.1+(x_0+x_1+x_2+(2*x_3)+(<blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">2*x_4)+(2*x_5)))^2)<br>
constraints:<br>
variables:<br>
x_0 [ 0 , 1 ]<br>
x_1 [ 0 , 1 ]<br>
x_2 [ 0 , 1 ]<br>
x_3 [ 0 , 1 ]<br>
x_4 [ 0 , 1 ]<br>
x_5 [ 0 , 1 ]<br>
end<br>
Problem size before reformulation: 6 variables (0 integer), 0 constraints.<br>
Problem size after reformulation: 8 variables (0 integer), 0 constraints.<br>
<br>
NLP0012I<br>
Num Status Obj It time<br>
NLP0013I 1 OPT 7.24915497916231e-16 8 0.008001<br>
Cbc0012I Integer solution of 7.24915e-16 found by Init Rounding NLP after 0 iterations and 0 nodes (0.00 seconds)<br>
NLP0013I 2 OPT 1.230414883748645e-20 3 0.004<br>
Cbc0001I Search completed - best objective 7.24915497916231e-16, took 0 iterations and 0 nodes (0.00 seconds)<br>
Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost<br>
<br>
couenne Optimal<br>
<br>
"Finished"<br>
<br>
<br>
[pbelotti ~] couenne testb<br>
<br>
objectives:<br>
min ((-0.1+(x_0+x_1+x_2))^2)<br>
constraints:<br>
( +1*x_8 +1*x_7 +1*x_3 -1*x_0) = 0<br>
( +1*x_8 +1*x_6 +1*x_4 -1*x_1) = 0<br>
( +1*x_7 +1*x_6 +1*x_5 -1*x_2) = 0<br>
variables:<br>
x_0 [ 0 , 3 ]<br>
x_1 [ 0 , 3 ]<br>
x_2 [ 0 , 3 ]<br>
x_3 [ 0 , 1 ]<br>
x_4 [ 0 , 1 ]<br>
x_5 [ 0 , 1 ]<br>
x_6 [ 0 , 1 ]<br>
x_7 [ 0 , 1 ]<br>
x_8 [ 0 , 1 ]<br>
end<br>
Problem size before reformulation: 9 variables (0 integer), 3 constraints.<br>
Problem size after reformulation: 11 variables (0 integer), 0 constraints.<br>
<br>
******************************************************************************<br>
This program contains Ipopt, a library for large-scale nonlinear optimization.<br>
Ipopt is released as open source code under the Common Public License (CPL).<br>
For more information visit <a href="http://projects.coin-or.org/Ipopt" target="_blank">http://projects.coin-or.org/Ipopt</a><br>
******************************************************************************<br>
<br>
NLP0012I<br>
Num Status Obj It time<br>
NLP0013I 1 OPT 8.626481252066872e-18 4 0.004<br>
Cbc0012I Integer solution of 8.62648e-18 found by Init Rounding NLP after 0 iterations and 0 nodes (0.00 seconds)<br>
NLP0013I 2 OPT 2.593450360578931e-25 4 0.004<br>
Cbc0001I Search completed - best objective 8.626481252066872e-18, took 0 iterations and 0 nodes (0.00 seconds)<br>
Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost<br>
<br>
couenne Optimal<br>
<br>
"Finished"<div><div class="h5"><br></div></div></blockquote><br>