<div dir="ltr"><div><br></div>Hi All, I am running csdp in Apache Pig (on hadoop actually), it works well, but the issue is that I need to convert blockmatrix to a string representation. Does anyone have any experience on this ? Thanks a lot<div>
<br></div><div>Hui <br><div><br></div><div><br></div></div></div><div class="gmail_extra"><br><br><div class="gmail_quote">On Fri, Nov 15, 2013 at 9:35 AM, Hui Wu <span dir="ltr"><<a href="mailto:wuhuing@gmail.com" target="_blank">wuhuing@gmail.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"> Thank Imre. Will try this solution.<span class="HOEnZb"><font color="#888888"><div><br></div><div>Hui</div>
</font></span></div><div class="HOEnZb"><div class="h5"><div class="gmail_extra"><br><br><div class="gmail_quote">On Fri, Nov 15, 2013 at 9:30 AM, Imre Pólik <span dir="ltr"><<a href="mailto:imre.polik@gmail.com" target="_blank">imre.polik@gmail.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">If your matrix X is actually rank 1, then it has a decomposition into z*z'. In this case only one eigenvalue is nonzero, and the others are zero.<div>
<br></div><div>The full eigenvalue decomposition is the sum of such rank-1 terms. </div>
<div><br></div><div>The basic fact is that the rank of X is the number of its nonzero eigenvalues (counted with multiplicities).</div><div>Imre</div></div><div class="gmail_extra"><div><div><br><br><div class="gmail_quote">
On Fri, Nov 15, 2013 at 12:26 PM, Hui Wu <span dir="ltr"><<a href="mailto:wuhuing@gmail.com" target="_blank">wuhuing@gmail.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><br><div>Hi Imre, thanks for your solution. Can you give me some references for explaining why that works ? </div>
<span><font color="#888888"><div><br></div><div>Hui</div></font></span></div><div><div><div class="gmail_extra"><br><br><div class="gmail_quote">
On Fri, Nov 15, 2013 at 9:07 AM, Imre Pólik <span dir="ltr"><<a href="mailto:imre.polik@gmail.com" target="_blank">imre.polik@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div dir="ltr">This means that you want a rank-1 solution for your problem. This in general is much harder than just solving an SDP. Your best bet is to perform an engeivalue decomposition and choose the eigenvector that blongs to the largest eigenvalue. If all the other eigenvalues are small, then you are fine.<div>
<br></div><div>Best,</div><div>Imre</div></div><div class="gmail_extra"><br><br><div class="gmail_quote">On Fri, Nov 15, 2013 at 12:00 PM, <span dir="ltr"><<a href="mailto:csdp-request@list.coin-or.org" target="_blank">csdp-request@list.coin-or.org</a>></span> wrote:<br>
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Today's Topics:<br>
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1. Re: SDP is dual infeasible (Wendel Melo)<br>
<br>
<br>
----------------------------------------------------------------------<br>
<br>
Message: 1<br>
Date: Fri, 15 Nov 2013 04:23:59 -0500<br>
From: Wendel Melo <<a href="mailto:wendelalexandre@gmail.com" target="_blank">wendelalexandre@gmail.com</a>><br>
To: Hui Wu <<a href="mailto:wuhuing@gmail.com" target="_blank">wuhuing@gmail.com</a>><br>
Cc: Brian Borchers <<a href="mailto:borchers.brian@gmail.com" target="_blank">borchers.brian@gmail.com</a>>, "<a href="mailto:csdp@list.coin-or.org" target="_blank">csdp@list.coin-or.org</a>"<br>
<<a href="mailto:csdp@list.coin-or.org" target="_blank">csdp@list.coin-or.org</a>><br>
Subject: Re: [Csdp] SDP is dual infeasible<br>
Message-ID:<br>
<CAATj=<a href="mailto:87UBTuRDhGNSbhLeW2tZFZ48a4uZMY_T5FzOKN9RkygPw@mail.gmail.com" target="_blank">87UBTuRDhGNSbhLeW2tZFZ48a4uZMY_T5FzOKN9RkygPw@mail.gmail.com</a>><br>
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<br>
Hi guys, one more question. After I get X, how can I get the vector of z,<br>
which satisfies z' * z = X. I tried Cholesky Decomposition in Matlab, it<br>
can only get an upper/lower triangular matrix. Any pkg to decompose X to a<br>
vector z ? Thanks<br>
<br>
I suppose that decomposition is not possible for all matrix X<br>
<br>
<br>
2013/11/15 Hui Wu <<a href="mailto:wuhuing@gmail.com" target="_blank">wuhuing@gmail.com</a>><br>
<br>
> Hi guys, one more question. After I get X, how can I get the vector of z,<br>
> which satisfies z' * z = X. I tried Cholesky Decomposition in Matlab, it<br>
> can only get an upper/lower triangular matrix. Any pkg to decompose X to a<br>
> vector z ? Thanks<br>
><br>
><br>
> Hui<br>
><br>
><br>
><br>
> On Thu, Nov 14, 2013 at 10:20 PM, Hui Wu <<a href="mailto:wuhuing@gmail.com" target="_blank">wuhuing@gmail.com</a>> wrote:<br>
><br>
>> Hi All, after adding one constraint, the SDP is successfully solved.<br>
>> Really appreciate all of you guys' analysis !<br>
>><br>
>> Hui<br>
>><br>
>><br>
>><br>
>> On Thu, Nov 14, 2013 at 5:24 PM, Hui Wu <<a href="mailto:wuhuing@gmail.com" target="_blank">wuhuing@gmail.com</a>> wrote:<br>
>><br>
>>> yeah good analysis.<br>
>>><br>
>>> If primal is feasible, as my input is primal form, does it mean that the<br>
>>> output solution is feasible ? Thanks<br>
>>><br>
>>> Hui<br>
>>><br>
>>><br>
>>> On Thu, Nov 14, 2013 at 5:22 PM, Brian Borchers <<br>
>>> <a href="mailto:borchers.brian@gmail.com" target="_blank">borchers.brian@gmail.com</a>> wrote:<br>
>>><br>
>>>><br>
>>>><br>
>>>><br>
>>>> On Thu, Nov 14, 2013 at 6:17 PM, Hui Wu <<a href="mailto:wuhuing@gmail.com" target="_blank">wuhuing@gmail.com</a>> wrote:<br>
>>>><br>
>>>>> One potential issue I can think about is the constraints are not<br>
>>>>> enough to make it bounded. I will add more constraints to see if it can be<br>
>>>>> feasible. Thanks again<br>
>>>>><br>
>>>><br>
>>>> It appears from the output that this problem is primal feasible and<br>
>>>> dual unbounded. Additional constrains could result in a problem with an<br>
>>>> optimal solution.<br>
>>>><br>
>>>>><br>
>>>>> Hui<br>
>>>>><br>
>>>>><br>
>>>>> On Thu, Nov 14, 2013 at 5:11 PM, Wendel Melo <<br>
>>>>> <a href="mailto:wendelalexandre@gmail.com" target="_blank">wendelalexandre@gmail.com</a>> wrote:<br>
>>>>><br>
>>>>>> Yes. But CSDP is declaring dual infeasibility. If the dual is<br>
>>>>>> infeasible, your (primal) problem can be unbounded or infeasible also.<br>
>>>>>><br>
>>>>>><br>
>>>>>> > If it is unbounded, then it needs more constraints, right ?<br>
>>>>>><br>
>>>>>> More or less. Maybe yes, but maybe you have a mistake on your<br>
>>>>>> objective function or in some constraint...<br>
>>>>>><br>
>>>>>><br>
>>>>>> 2013/11/14 Hui Wu <<a href="mailto:wuhuing@gmail.com" target="_blank">wuhuing@gmail.com</a>><br>
>>>>>><br>
>>>>>>><br>
>>>>>>> Hi Wendel, if it is unbounded, it means there is no optimal<br>
>>>>>>> solution, but there should have feasible solutions, right ?<br>
>>>>>>><br>
>>>>>>> Hui<br>
>>>>>>><br>
>>>>>>><br>
>>>>>>> On Thu, Nov 14, 2013 at 4:58 PM, Hui Wu <<a href="mailto:wuhuing@gmail.com" target="_blank">wuhuing@gmail.com</a>> wrote:<br>
>>>>>>><br>
>>>>>>>> I am not too sure ...<br>
>>>>>>>> If it is unbounded, then it needs more constraints, right ?<br>
>>>>>>>><br>
>>>>>>>> Appreciate your analysis !<br>
>>>>>>>><br>
>>>>>>>> Hui<br>
>>>>>>>><br>
>>>>>>>><br>
>>>>>>>> On Thu, Nov 14, 2013 at 4:56 PM, Wendel Melo <<br>
>>>>>>>> <a href="mailto:wendelalexandre@gmail.com" target="_blank">wendelalexandre@gmail.com</a>> wrote:<br>
>>>>>>>><br>
>>>>>>>>> Maybe your problem is unbounded and so, CSDP is declaring<br>
>>>>>>>>> infeasibility. (We can say primal objective function getting huge vaules<br>
>>>>>>>>> before CSDP stop).<br>
>>>>>>>>><br>
>>>>>>>>> Can you be sure your problem is not unbounded?<br>
>>>>>>>>><br>
>>>>>>>>><br>
>>>>>>>>> 2013/11/14 Hui Wu <<a href="mailto:wuhuing@gmail.com" target="_blank">wuhuing@gmail.com</a>><br>
>>>>>>>>><br>
>>>>>>>>>> resend after joining the mail list :)<br>
>>>>>>>>>> On Nov 13, 2013 9:51 PM, "Hui Wu" <<a href="mailto:wuhuing@gmail.com" target="_blank">wuhuing@gmail.com</a>> wrote:<br>
>>>>>>>>>><br>
>>>>>>>>>>> Hi Guys, I am using csdp's matlab interface for the following<br>
>>>>>>>>>>> sdp problem, which is described in the attachment. While I run the script,<br>
>>>>>>>>>>> I get<br>
>>>>>>>>>>><br>
>>>>>>>>>>> *>>[x, y, z] = genSample();*<br>
>>>>>>>>>>> *Number of constraints: 6 *<br>
>>>>>>>>>>> *Number of SDP blocks: 1 *<br>
>>>>>>>>>>> *Number of LP vars: 0 *<br>
>>>>>>>>>>> *C block 1, blocksize, 6*<br>
>>>>>>>>>>> *Checking constraint 1 *<br>
>>>>>>>>>>> *Checking constraint 2 *<br>
>>>>>>>>>>> *Checking constraint 3 *<br>
>>>>>>>>>>> *Checking constraint 4 *<br>
>>>>>>>>>>> *Checking constraint 5 *<br>
>>>>>>>>>>> *Checking constraint 6 *<br>
>>>>>>>>>>> *Iter: 0 Ap: 0.00e+00 Pobj: 0.0000000e+00 Ad: 0.00e+00 Dobj:<br>
>>>>>>>>>>> 0.0000000e+00 *<br>
>>>>>>>>>>> *Iter: 1 Ap: 1.00e+00 Pobj: 2.4901133e+04 Ad: 6.77e-01 Dobj:<br>
>>>>>>>>>>> 3.0972415e+03 *<br>
>>>>>>>>>>> *Iter: 2 Ap: 1.00e+00 Pobj: 1.7734229e+05 Ad: 5.18e-01 Dobj:<br>
>>>>>>>>>>> 1.6715331e+02 *<br>
>>>>>>>>>>> *Iter: 3 Ap: 2.10e-02 Pobj: 9.3394935e+05 Ad: 2.66e-02 Dobj:<br>
>>>>>>>>>>> 1.2916856e+03 *<br>
>>>>>>>>>>> *Iter: 4 Ap: 1.00e+00 Pobj: 5.7585163e+07 Ad: 1.05e-01 Dobj:<br>
>>>>>>>>>>> 1.0092369e+03 *<br>
>>>>>>>>>>> *Iter: 5 Ap: 2.82e-03 Pobj: 5.3050644e+08 Ad: 2.97e-03 Dobj:<br>
>>>>>>>>>>> 8.2813968e+02 *<br>
>>>>>>>>>>> *Iter: 6 Ap: 1.29e-03 Pobj: 2.8396651e+09 Ad: 2.90e-03 Dobj:<br>
>>>>>>>>>>> 9.6682104e+02 *<br>
>>>>>>>>>>> *Declaring dual infeasibility.*<br>
>>>>>>>>>>> *Success: SDP is dual infeasible*<br>
>>>>>>>>>>> *Certificate of dual infeasibility: tr(CX)=1.00000e+00,<br>
>>>>>>>>>>> ||A(X)||=4.91757e-09*<br>
>>>>>>>>>>> *Elements time: 0.000010 *<br>
>>>>>>>>>>> *Factor time: 0.000045 *<br>
>>>>>>>>>>> *Other time: 0.000882 *<br>
>>>>>>>>>>> *Total time: 0.000937 *<br>
>>>>>>>>>>><br>
>>>>>>>>>>> Can some body help tell me why my SDP is dual infeasible ? Is it<br>
>>>>>>>>>>> because there is something wrong with my problem setting or it is normal to<br>
>>>>>>>>>>> my SDP? Thanks<br>
>>>>>>>>>>><br>
>>>>>>>>>>> Hui<br>
>>>>>>>>>>><br>
>>>>>>>>>>><br>
>>>>>>>>>> _______________________________________________<br>
>>>>>>>>>> Csdp mailing list<br>
>>>>>>>>>> <a href="mailto:Csdp@list.coin-or.org" target="_blank">Csdp@list.coin-or.org</a><br>
>>>>>>>>>> <a href="http://list.coin-or.org/mailman/listinfo/csdp" target="_blank">http://list.coin-or.org/mailman/listinfo/csdp</a><br>
>>>>>>>>>><br>
>>>>>>>>>><br>
>>>>>>>>><br>
>>>>>>>>><br>
>>>>>>>>> --<br>
>>>>>>>>> Wendel<br>
>>>>>>>>><br>
>>>>>>>><br>
>>>>>>>><br>
>>>>>>><br>
>>>>>><br>
>>>>>><br>
>>>>>> --<br>
>>>>>> Wendel<br>
>>>>>><br>
>>>>><br>
>>>>><br>
>>>>> _______________________________________________<br>
>>>>> Csdp mailing list<br>
>>>>> <a href="mailto:Csdp@list.coin-or.org" target="_blank">Csdp@list.coin-or.org</a><br>
>>>>> <a href="http://list.coin-or.org/mailman/listinfo/csdp" target="_blank">http://list.coin-or.org/mailman/listinfo/csdp</a><br>
>>>>><br>
>>>>><br>
>>>><br>
>>><br>
>><br>
><br>
<br>
<br>
--<br>
Wendel<br>
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