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<div data-externalstyle="false" dir="ltr" style="font-family: 'Calibri', 'Segoe UI', 'Meiryo', 'Microsoft YaHei UI', 'Microsoft JhengHei UI', 'Malgun Gothic', 'sans-serif';font-size:12pt;"><div>Thanks for your response. </div><div><br></div><div>I was using this text file as a reference: <a href="http://plato.asu.edu/ftp/sdpa_format.txt" target="_parent">http://plato.asu.edu/ftp/sdpa_format.txt</a> </div><div>If I am interpreting your response correctly, that file has reversed the roles of primal and dual with respect to CSDP’s implementation. </div><div><br></div><div style="padding-top: 5px; border-top-color: rgb(229, 229, 229); border-top-width: 1px; border-top-style: solid;"><div><font face=" 'Calibri', 'Segoe UI', 'Meiryo', 'Microsoft YaHei UI', 'Microsoft JhengHei UI', 'Malgun Gothic', 'sans-serif'" style='line-height: 15pt; letter-spacing: 0.02em; font-family: "Calibri", "Segoe UI", "Meiryo", "Microsoft YaHei UI", "Microsoft JhengHei UI", "Malgun Gothic", "sans-serif"; font-size: 12pt;'><b>From:</b> <a href="mailto:borchers@nmt.edu" target="_parent">Brian Borchers</a><br><b>Sent:</b> Monday, November 24, 2014 6:46 PM<br><b>To:</b> <a href="mailto:markisus@gmail.com" target="_parent">Mark Liu</a><br><b>Cc:</b> <a href="mailto:csdp@list.coin-or.org" target="_parent">csdp@list.coin-or.org</a></font></div></div><div><br></div><div dir=""><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="_parent">markisus@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; padding-left: 1ex; border-left-color: rgb(204, 204, 204); border-left-width: 1px; border-left-style: solid;">
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<div>I have posted this question to <a href="http://cs.stackexchange.com" target="_parent">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="_parent">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; font-size-adjust: none; font-stretch: 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; border-image: none; 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; font-size-adjust: none; font-stretch: 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="_parent">borchers@nmt.edu</a><br>Department of Mathematics <a href="http://www.nmt.edu/~borchers/" target="_parent">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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