<html>
<head>
<meta name="generator" content="Windows Mail 17.5.9600.20689">
<style data-externalstyle="true"><!--
p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph {
margin-top:0in;
margin-right:0in;
margin-bottom:0in;
margin-left:.5in;
margin-bottom:.0001pt;
}
p.MsoNormal, li.MsoNormal, div.MsoNormal {
margin:0in;
margin-bottom:.0001pt;
}
p.MsoListParagraphCxSpFirst, li.MsoListParagraphCxSpFirst, div.MsoListParagraphCxSpFirst,
p.MsoListParagraphCxSpMiddle, li.MsoListParagraphCxSpMiddle, div.MsoListParagraphCxSpMiddle,
p.MsoListParagraphCxSpLast, li.MsoListParagraphCxSpLast, div.MsoListParagraphCxSpLast {
margin-top:0in;
margin-right:0in;
margin-bottom:0in;
margin-left:.5in;
margin-bottom:.0001pt;
line-height:115%;
}
--></style></head>
<body dir="ltr">
<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>Thank you for your help!</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> Thursday, December 4, 2014 9:39 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"><br><div class="gmail_extra"><br><div class="gmail_quote">On Thu, Dec 4, 2014 at 7:10 PM, Brian Borchers <span dir="ltr"><<a href="mailto:borchers@nmt.edu" target="_parent">borchers@nmt.edu</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;"><div dir="ltr">At each iteration of the primal-dual interior point method, a large, dense, symmetric and positive definite system of equations is solved to obtain the steps deltaX, deltay, and deltaZ. When this error case occurs, it indicates that this system of equations is singular and can't be solved. <div><br></div><div>This could be the result of a bug in CSDP or a problem with the formulation of your SDP. If you would be willing to send me a copy of the problem on which this error occurs, I'd be happy to investigate the cause. <br></div></div><div class="gmail_extra"><br><div class="gmail_quote"><div><div>On Thu, Dec 4, 2014 at 3:59 PM, <span dir="ltr"><<a href="mailto:markisus@gmail.com" target="_parent">markisus@gmail.com</a>></span> wrote:<br></div></div><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;"><div><div>
<div dir="ltr">
<div style='font-family: Calibri,"Segoe UI",Meiryo,"Microsoft YaHei UI","Microsoft JhengHei UI","Malgun Gothic",sans-serif; font-size: 12pt;' dir="ltr">
<div><div>What does this error mean? Which matrix is the system matrix and why would singularity be a problem?</div><div><br></div><div>If it helps, here is my input file:<br></div></div><div><div><a href="http://pastebin.com/ite3C1Vz" target="_parent">http://pastebin.com/ite3C1Vz</a></div></div></div></div></div></div></blockquote></div></div></blockquote><div><br></div><div>After looking at your problem, it's clear that the difficulty is that you have linearly dependent constraints. Although your problem has 30 constraints, there are only 18 linearly independent constraints. The algorithm assumes that you have formulated your problem without linearly dependent constraints- you'll have to remove the redundant constraints before passing the problem to CSDP. </div><div><br></div><div>I'm attaching a version of your problem where I've removed the linearly dependent constraints. This solves quite easily:</div><div><div><br></div><div>> csdp testprob2.dat-s</div><div>This is a pure dual feasibility problem.</div><div>Iter: 0 Ap: 0.00e+00 Pobj: 9.1126984e+01 Ad: 0.00e+00 Dobj: 0.0000000e+00 </div><div>Iter: 1 Ap: 9.60e-01 Pobj: 3.6097681e+00 Ad: 9.60e-01 Dobj: 0.0000000e+00 </div><div>Iter: 2 Ap: 9.60e-01 Pobj: 1.4298925e-01 Ad: 9.60e-01 Dobj: 0.0000000e+00 </div><div>Iter: 3 Ap: 9.58e-01 Pobj: 6.0555298e-03 Ad: 9.58e-01 Dobj: 0.0000000e+00 </div><div>Iter: 4 Ap: 9.57e-01 Pobj: 2.5759669e-04 Ad: 9.58e-01 Dobj: 0.0000000e+00 </div><div>Iter: 5 Ap: 9.57e-01 Pobj: 1.0961309e-05 Ad: 9.59e-01 Dobj: 0.0000000e+00 </div><div>Iter: 6 Ap: 9.57e-01 Pobj: 4.6643796e-07 Ad: 9.97e-01 Dobj: 0.0000000e+00 </div><div>Iter: 7 Ap: 9.57e-01 Pobj: 1.9848423e-08 Ad: 9.69e-01 Dobj: 0.0000000e+00 </div><div>Iter: 8 Ap: 9.57e-01 Pobj: 8.4461375e-10 Ad: 9.60e-01 Dobj: 0.0000000e+00 </div><div>Success: SDP solved</div><div>Primal objective value: 1.0000000e-40 </div><div>Dual objective value: 0.0000000e+00 </div><div>Relative primal infeasibility: 1.41e-39 </div><div>Relative dual infeasibility: 9.72e-10 </div><div>Real Relative Gap: -1.00e-40 </div><div>XZ Relative Gap: 3.48e-37 </div><div>DIMACS error measures: 1.41e-39 0.00e+00 9.72e-10 0.00e+00 -1.00e-40 3.48e-37</div><div>Elements time: 0.001023 </div><div>Factor time: 0.000078 </div><div>Other time: 0.005480 </div><div>Total time: 0.006581 </div></div><div><br></div><div><br></div></div><br clear="all"><div><br></div>-- <br><div>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: <a href="tel:%28575%29%20322-2592" target="_parent">(575) 322-2592</a><br>Socorro, NM 87801 FAX: <a href="tel:%28575%29%20835-5366" target="_parent">(575) 835-5366</a></div>
</div></div>
</div></div>
</body>
</html>