[Csdp] Why would this Semidefinite Program be Dual Infeasible?

[markisus at gmail.com]

Thanks for your response. 


I was using this text file as a reference: http://plato.asu.edu/ftp/sdpa_format.txt 

If I am interpreting your response correctly, that file has reversed the roles of primal and dual with respect to CSDP’s implementation. 





From: Brian Borchers
Sent: ‎Monday‎, ‎November‎ ‎24‎, ‎2014 ‎6‎:‎46‎ ‎PM
To: Mark Liu
Cc: csdp at list.coin-or.org





Perhaps there is some confusion here about "primal" versus "dual".  The primal problem here is the one with two constraints that trace(A1*X)=0 and trace(A2*X)=0.  Setting X=0 satisfies those constraints and provides a primal feasible solution.  There are actually infinitely many primal feasible solutions.  The issue here is that the primal SDP is unbounded and the dual problem is infeasible.  



On Mon, Nov 24, 2014 at 3:54 PM, <markisus at gmail.com> wrote:




I have posted this question to cs.stackexchange.com but then I thought maybe this mailing list is the better audience. I am new to CSDP and SDPs in general, so I’m not sure if my problem is a misunderstanding of SDPs or the software CSDP. CSDP is telling me that my problem is dual infeasible, even though setting all variables to 0 should provide a feasible solution. This is because I only have two constraints, L1 = 0 and L2 = 0, where L1 and L2 are linear functions of my variables Xij. 




Here is my program in SPDA format, where I am focusing on the dual problem:




    2
    1
    11
    0.0 0.0
    0 1 1 10 1.0
    1 1 1 10 .25
    1 1 3 10 .25
    1 1 6 10 -.25
    1 1 8 10 -.25
    1 1 9 10 -.5
    2 1 2 11 -3.0
    2 1 3 11 -4.0
    2 1 4 11 1.0
    2 1 5 11 1.0
    2 1 6 11 -4.0
    2 1 7 11 3.0
    2 1 9 11 1.0







Below is a link to my stackexchange post:

http://cs.stackexchange.com/questions/33478/why-would-this-semidefinite-program-be-dual-infeasible













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-- 

Brian Borchers                          borchers at nmt.edu
Department of Mathematics      http://www.nmt.edu/~borchers/
New Mexico Tech                       Phone: (575) 322-2592
Socorro, NM 87801                   FAX: (575) 835-5366
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