[Csdp] Csdp Digest, Vol 27, Issue 4

Hui Wu wuhuing at gmail.com
Fri Nov 15 12:26:34 EST 2013 

Hi Imre, thanks for your solution. Can you give me some references for
explaining why that works ?

Hui


On Fri, Nov 15, 2013 at 9:07 AM, Imre Pólik <imre.polik at gmail.com> wrote:

> 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.
>
> Best,
> Imre
>
>
> On Fri, Nov 15, 2013 at 12:00 PM, <csdp-request at list.coin-or.org> wrote:
>
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>> Today's Topics:
>>
>>    1. Re: SDP is dual infeasible (Wendel Melo)
>>
>>
>> ----------------------------------------------------------------------
>>
>> Message: 1
>> Date: Fri, 15 Nov 2013 04:23:59 -0500
>> From: Wendel Melo <wendelalexandre at gmail.com>
>> To: Hui Wu <wuhuing at gmail.com>
>> Cc: Brian Borchers <borchers.brian at gmail.com>,  "csdp at list.coin-or.org"
>>         <csdp at list.coin-or.org>
>> Subject: Re: [Csdp] SDP is dual infeasible
>> Message-ID:
>>         <CAATj=
>> 87UBTuRDhGNSbhLeW2tZFZ48a4uZMY_T5FzOKN9RkygPw at mail.gmail.com>
>> Content-Type: text/plain; charset="iso-8859-1"
>>
>> Hi guys, one more question. After I get X, how can I get the vector of z,
>> which satisfies z' * z = X. I tried Cholesky Decomposition in Matlab, it
>> can only get an upper/lower triangular matrix. Any pkg to decompose X to a
>> vector z ? Thanks
>>
>> I suppose that decomposition is not possible for all matrix X
>>
>>
>> 2013/11/15 Hui Wu <wuhuing at gmail.com>
>>
>> > Hi guys, one more question. After I get X, how can I get the vector of
>> z,
>> > which satisfies z' * z = X. I tried Cholesky Decomposition in Matlab, it
>> > can only get an upper/lower triangular matrix. Any pkg to decompose X
>> to a
>> > vector z ? Thanks
>> >
>> >
>> > Hui
>> >
>> >
>> >
>> > On Thu, Nov 14, 2013 at 10:20 PM, Hui Wu <wuhuing at gmail.com> wrote:
>> >
>> >> Hi All, after adding one constraint, the SDP is successfully solved.
>> >> Really appreciate all of you guys' analysis !
>> >>
>> >> Hui
>> >>
>> >>
>> >>
>> >> On Thu, Nov 14, 2013 at 5:24 PM, Hui Wu <wuhuing at gmail.com> wrote:
>> >>
>> >>> yeah good analysis.
>> >>>
>> >>> If primal is feasible, as my input is primal form, does it mean that
>> the
>> >>> output solution is feasible ? Thanks
>> >>>
>> >>> Hui
>> >>>
>> >>>
>> >>> On Thu, Nov 14, 2013 at 5:22 PM, Brian Borchers <
>> >>> borchers.brian at gmail.com> wrote:
>> >>>
>> >>>>
>> >>>>
>> >>>>
>> >>>> On Thu, Nov 14, 2013 at 6:17 PM, Hui Wu <wuhuing at gmail.com> wrote:
>> >>>>
>> >>>>> One potential issue I can think about is the constraints are not
>> >>>>> enough to make it bounded. I will add more constraints to see if it
>> can be
>> >>>>> feasible. Thanks again
>> >>>>>
>> >>>>
>> >>>> It appears from the output that this problem is primal feasible and
>> >>>> dual unbounded.  Additional constrains could result in a problem
>> with an
>> >>>> optimal solution.
>> >>>>
>> >>>>>
>> >>>>> Hui
>> >>>>>
>> >>>>>
>> >>>>> On Thu, Nov 14, 2013 at 5:11 PM, Wendel Melo <
>> >>>>> wendelalexandre at gmail.com> wrote:
>> >>>>>
>> >>>>>> Yes. But CSDP is declaring dual infeasibility. If the dual is
>> >>>>>> infeasible, your (primal) problem can be unbounded or infeasible
>> also.
>> >>>>>>
>> >>>>>>
>> >>>>>> > If it is unbounded, then it needs more constraints, right ?
>> >>>>>>
>> >>>>>> More or less. Maybe yes, but maybe you have a mistake on your
>> >>>>>> objective function or in some constraint...
>> >>>>>>
>> >>>>>>
>> >>>>>> 2013/11/14 Hui Wu <wuhuing at gmail.com>
>> >>>>>>
>> >>>>>>>
>> >>>>>>> Hi Wendel, if it is unbounded, it means there is no optimal
>> >>>>>>> solution, but there should have feasible solutions, right ?
>> >>>>>>>
>> >>>>>>> Hui
>> >>>>>>>
>> >>>>>>>
>> >>>>>>> On Thu, Nov 14, 2013 at 4:58 PM, Hui Wu <wuhuing at gmail.com>
>> wrote:
>> >>>>>>>
>> >>>>>>>> I am not too sure ...
>> >>>>>>>> If it is unbounded, then it needs more constraints, right ?
>> >>>>>>>>
>> >>>>>>>> Appreciate your analysis !
>> >>>>>>>>
>> >>>>>>>> Hui
>> >>>>>>>>
>> >>>>>>>>
>> >>>>>>>> On Thu, Nov 14, 2013 at 4:56 PM, Wendel Melo <
>> >>>>>>>> wendelalexandre at gmail.com> wrote:
>> >>>>>>>>
>> >>>>>>>>> Maybe your problem is unbounded and so, CSDP is declaring
>> >>>>>>>>> infeasibility. (We can say primal objective function getting
>> huge vaules
>> >>>>>>>>> before CSDP stop).
>> >>>>>>>>>
>> >>>>>>>>> Can you be sure your problem is not unbounded?
>> >>>>>>>>>
>> >>>>>>>>>
>> >>>>>>>>> 2013/11/14 Hui Wu <wuhuing at gmail.com>
>> >>>>>>>>>
>> >>>>>>>>>>  resend after joining the mail list :)
>> >>>>>>>>>> On Nov 13, 2013 9:51 PM, "Hui Wu" <wuhuing at gmail.com> wrote:
>> >>>>>>>>>>
>> >>>>>>>>>>> Hi Guys, I am using csdp's matlab interface for the following
>> >>>>>>>>>>> sdp problem, which is described in the attachment. While I
>> run the script,
>> >>>>>>>>>>> I get
>> >>>>>>>>>>>
>> >>>>>>>>>>> *>>[x, y, z] = genSample();*
>> >>>>>>>>>>> *Number of constraints: 6 *
>> >>>>>>>>>>> *Number of SDP blocks: 1 *
>> >>>>>>>>>>> *Number of LP vars: 0 *
>> >>>>>>>>>>> *C block 1, blocksize, 6*
>> >>>>>>>>>>> *Checking constraint 1 *
>> >>>>>>>>>>> *Checking constraint 2 *
>> >>>>>>>>>>> *Checking constraint 3 *
>> >>>>>>>>>>> *Checking constraint 4 *
>> >>>>>>>>>>> *Checking constraint 5 *
>> >>>>>>>>>>> *Checking constraint 6 *
>> >>>>>>>>>>> *Iter:  0 Ap: 0.00e+00 Pobj:  0.0000000e+00 Ad: 0.00e+00 Dobj:
>> >>>>>>>>>>>  0.0000000e+00 *
>> >>>>>>>>>>> *Iter:  1 Ap: 1.00e+00 Pobj:  2.4901133e+04 Ad: 6.77e-01 Dobj:
>> >>>>>>>>>>>  3.0972415e+03 *
>> >>>>>>>>>>> *Iter:  2 Ap: 1.00e+00 Pobj:  1.7734229e+05 Ad: 5.18e-01 Dobj:
>> >>>>>>>>>>>  1.6715331e+02 *
>> >>>>>>>>>>> *Iter:  3 Ap: 2.10e-02 Pobj:  9.3394935e+05 Ad: 2.66e-02 Dobj:
>> >>>>>>>>>>>  1.2916856e+03 *
>> >>>>>>>>>>> *Iter:  4 Ap: 1.00e+00 Pobj:  5.7585163e+07 Ad: 1.05e-01 Dobj:
>> >>>>>>>>>>>  1.0092369e+03 *
>> >>>>>>>>>>> *Iter:  5 Ap: 2.82e-03 Pobj:  5.3050644e+08 Ad: 2.97e-03 Dobj:
>> >>>>>>>>>>>  8.2813968e+02 *
>> >>>>>>>>>>> *Iter:  6 Ap: 1.29e-03 Pobj:  2.8396651e+09 Ad: 2.90e-03 Dobj:
>> >>>>>>>>>>>  9.6682104e+02 *
>> >>>>>>>>>>> *Declaring dual infeasibility.*
>> >>>>>>>>>>> *Success: SDP is dual infeasible*
>> >>>>>>>>>>> *Certificate of dual infeasibility: tr(CX)=1.00000e+00,
>> >>>>>>>>>>> ||A(X)||=4.91757e-09*
>> >>>>>>>>>>> *Elements time: 0.000010 *
>> >>>>>>>>>>> *Factor time: 0.000045 *
>> >>>>>>>>>>> *Other time: 0.000882 *
>> >>>>>>>>>>> *Total time: 0.000937 *
>> >>>>>>>>>>>
>> >>>>>>>>>>> Can some body help tell me why my SDP is dual infeasible ? Is
>> it
>> >>>>>>>>>>> because there is something wrong with my problem setting or
>> it is normal to
>> >>>>>>>>>>> my SDP? Thanks
>> >>>>>>>>>>>
>> >>>>>>>>>>> Hui
>> >>>>>>>>>>>
>> >>>>>>>>>>>
>> >>>>>>>>>> _______________________________________________
>> >>>>>>>>>> Csdp mailing list
>> >>>>>>>>>> Csdp at list.coin-or.org
>> >>>>>>>>>> http://list.coin-or.org/mailman/listinfo/csdp
>> >>>>>>>>>>
>> >>>>>>>>>>
>> >>>>>>>>>
>> >>>>>>>>>
>> >>>>>>>>> --
>> >>>>>>>>> Wendel
>> >>>>>>>>>
>> >>>>>>>>
>> >>>>>>>>
>> >>>>>>>
>> >>>>>>
>> >>>>>>
>> >>>>>> --
>> >>>>>> Wendel
>> >>>>>>
>> >>>>>
>> >>>>>
>> >>>>> _______________________________________________
>> >>>>> Csdp mailing list
>> >>>>> Csdp at list.coin-or.org
>> >>>>> http://list.coin-or.org/mailman/listinfo/csdp
>> >>>>>
>> >>>>>
>> >>>>
>> >>>
>> >>
>> >
>>
>>
>> --
>> Wendel
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>> End of Csdp Digest, Vol 27, Issue 4
>> ***********************************
>>
>
>
>
> --
> http://imre.polik.net
>
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