<div dir="ltr"><div>Dear Damien,<br><br>I could reproduce the behavior you describe. I am not sure why this happens, but I suspect it may have to do with 1) the coefficients you use and 2) the structure of the problem. Regarding the latter, the feasible set seems to be a very thin region around the segment from (l1,l2) to (u1,u2) as you can see by plotting both functions. <br>
<br>Even trickier, the objective function has a zero eigenvalue on the same direction as the segment. I think all of this makes Couenne believe that the first solution found is the optimal one; I would need to investigate this further, but I suppose the subsequent bound tightening restricts the feasible set around the solution found. Although the difference in objective function values are more than COUENNE_EPS, in practice Couenne does not find anything better from then on.<br>
<br></div>This is a nice test problem for the numerical stability of solvers such as Couenne.<br><div><br></div><div>Pietro<br><br></div></div><div class="gmail_extra"><br><br><div class="gmail_quote">On Tue, May 6, 2014 at 12:49 AM, Damien Gerard <span dir="ltr"><<a href="mailto:damien.gerard@ulg.ac.be" target="_blank">damien.gerard@ulg.ac.be</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Dear all,<br>
<br>
If I run some models with different tree search strategies and node comparison methods, I sometimes end up with a difference in the optimal objective value which is bigger than COUENNE_EPS=1.e-07. Let me illustrate this with a small model - a continuous qcqp with 2 variables :<br>
<br>
top node & best bound : f* = -0.007036, x0 = 0.0617, x1 = 0.0374<br>
top node & best guess : f* = -0.007066, x0 = 0.0624, x1 = 0.0382<br>
<br>
Does anybody has any clue why such a difference ?<br>
<br>
Thank you very much and thanks to all the Couenne contributors for the great work !<br>
<br>
Best regards,<br>
<br>
Damien Gerard<br>
<br>
<br>
-- problem in AMPL format, solved with Couenne 0.4 --<br>
<br>
var X0 >= -0.175464, <= 0.088790;<br>
var X1 >= -0.205315, <= 0.088286;<br>
minimize f : X0^2 * -1.942191249 + X1^2 * -1.942191249 + 3.884382497 * X0 * X1 - 0.005870047836474;<br>
subject to ctr01 : X0^2 * 1.942191249 - 1.942191249 * X0 * X1 - 10.035428230507371 * X1 + 9.457590773272191 * X0 + 1.458281314539863 - 1.942191249 * 0.9547837317091492 * 0.8998075223169929 <= 0;<br>
subject to ctr02 : X0^2 * 10.51068205 + -1.747598295628436 * X0 + -10.51068205 * X0 * X1 + 1.942191249 * 0.9547837317091492 * X1 + 9.052213345123171 - 9.029953811482843 <= 0;<br>
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</blockquote></div><br></div>