<div dir="ltr">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. </div><div class="gmail_extra"><br><div class="gmail_quote">On Mon, Nov 24, 2014 at 3:54 PM, <span dir="ltr"><<a href="mailto:markisus@gmail.com" target="_blank">markisus@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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<div>I have posted this question to <a href="http://cs.stackexchange.com" target="_blank">cs.stackexchange.com</a> 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. </div><div><br></div><div>Here is my program in SPDA format, where I am focusing on the dual problem:</div><div><br></div><div> 2<br> 1<br> 11<br> 0.0 0.0<br> 0 1 1 10 1.0<br> 1 1 1 10 .25<br> 1 1 3 10 .25<br> 1 1 6 10 -.25<br> 1 1 8 10 -.25<br> 1 1 9 10 -.5<br> 2 1 2 11 -3.0<br> 2 1 3 11 -4.0<br> 2 1 4 11 1.0<br> 2 1 5 11 1.0<br> 2 1 6 11 -4.0<br> 2 1 7 11 3.0<br> 2 1 9 11 1.0</div><div><br></div><div><br></div><div>Below is a link to my stackexchange post:</div><div><a href="http://cs.stackexchange.com/questions/33478/why-would-this-semidefinite-program-be-dual-infeasible" target="_blank">http://cs.stackexchange.com/questions/33478/why-would-this-semidefinite-program-be-dual-infeasible</a></div><span style="font:14px/19.6px "Helvetica Neue",Arial,sans-serif;text-align:left;color:rgb(17,17,17);text-transform:none;text-indent:0px;letter-spacing:normal;word-spacing:0px;float:none;display:inline!important;white-space:normal;background-color:rgb(253,253,253)"><div><br></div><div><br></div><p style="font:14px/19.6px "Helvetica Neue",Arial,sans-serif;margin:0px 0px 1em;padding:0px;border:0px black;text-align:left;color:rgb(17,17,17);text-transform:none;text-indent:0px;letter-spacing:normal;clear:both;word-spacing:0px;vertical-align:baseline;white-space:normal;background-color:rgb(253,253,253)"><span></span><br></p></span><div><br></div>
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<br></blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="gmail_signature">Brian Borchers <a href="mailto:borchers@nmt.edu" target="_blank">borchers@nmt.edu</a><br>Department of Mathematics <a href="http://www.nmt.edu/~borchers/" target="_blank">http://www.nmt.edu/~borchers/</a><br>New Mexico Tech Phone: (575) 322-2592<br>Socorro, NM 87801 FAX: (575) 835-5366</div>
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