[Csdp] Csdp Digest, Vol 27, Issue 4

Imre Pólik imre.polik at gmail.com
Fri Nov 15 12:07:13 EST 2013 

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:
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>    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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