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John,<br><br>
Thanks for looking into it and quickly replying to my question.<br><br>
I've not verified that the objective function (f) is nonconvex. Whether
it's convex or not, the solution (N0C0=N1C0=N2C0=N3C0=1 and
N0C1=N1C1=N2C1=N3C1=0) shouldn't be a local minimum because the gradient
of f is not a 0-vector at this point. (The partial derivative wrt N0C0 =
1-8+4+2= -1.) <br><br>
Is it possible that something in CbcModel has caused the B&B process
to stop prematurely?<br><br>
Best regards,<br><br>
Yiming<br><br>
<br>
At 11:46 AM 3/9/2006, John J Forrest wrote:<br><br>
<blockquote type=cite class=cite cite=""><font size=2>Yiming,</font>
<br><br>
<font size=2>The problem does not seem to be convex and the solution giving 0.0 is a local optimum.</font> <br><br>
<font size=2>John Forrest</font> <br><br>
<br>
<font size=1><b>Yiming Yao <yao3@llnl.gov></b> </font><br>
<font size=1>Sent by: coin-lpsolver-bounces@list.coin-or.org</font> <br><br>
<font size=1>03/08/2006 08:56 PM</font> <br>
<div align="right"><font size=1>To<br>
</div>
<coin-lpsolver@list.coin-or.org>, John J Forrest/Watson/IBM@IBMUS</font> <br>
<div align="right"><font size=1>cc<br>
Subject<br>
</div>
[Coin-lpsolver] COIN/Cbc/Samples/qmip.cpp</font> <br><br>
<br><br>
<br>
I tried to use qmip.cpp in Cbc/Samples (downloaded March 7) to solve a simple quadratic 0-1 integer program (qmip1.mps) and got the following solution:<br><br>
N0C0=N1C0=N2C0=N3C0=1 and min obj = 0<br><br>
This is not the minimum solution. Either N0C0=N1C0=N2C1=N3C1=1 or N0C1=N1C1=N2C0=N3C1=1 will result in obj = -6<br><br>
Would you take a look at it and see what's gone wrong?<br><br>
As an experiment, I made the coefficient of the N0C0*N1C0 in the objective function very large relative to other terms (see qmip2.mps), preventing N0C0 and N1C0 from being 1 at the same time, qmip then produced a correct answer: N0C1=N1C1=N2C0=N3C1=1 with obj = -6.<br>
<font face="Courier New, Courier"><br>
The variables are indexed as below:<br>
0 N0C0<br>
1 N0C1<br>
2 N1C0<br>
3 N1C1<br>
4 N2C0<br>
5 N2C1<br>
6 N3C0<br>
7 N3C1<br>
</font><br>
Thanks,<br><br>
Yiming<br><br>
----------------------------------------------------------------<br>
Yiming Yao <br>
Systems & Decision Sciences Section yao3@llnl.gov <br>
Lawrence Livermore National Laboratory Tel: 925-422-1922 <br>
7000 East Avenue, L-377<br>
Livermore, CA 94550<br>
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