<div dir="ltr"><br><div class="gmail_extra"><br><div class="gmail_quote">On Tue, Jul 7, 2015 at 9:56 AM, Jingyu He <span dir="ltr"><<a href="mailto:jingyuhe@hotmail.com" target="_blank">jingyuhe@hotmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div><div dir="ltr"><span style="color:rgb(68,68,68);font-size:15px;line-height:21.2999992370605px;background-color:rgb(255,255,255)">Hi all,</span><div style="line-height:21.2999992370605px;color:rgb(68,68,68);font-size:15px;background-color:rgb(255,255,255)"><br style="line-height:21.2999992370605px"></div><div style="line-height:21.2999992370605px;color:rgb(68,68,68);font-size:15px;background-color:rgb(255,255,255)">Sorry, there is a little typo in the last email. I correct it here.</div><div style="line-height:21.2999992370605px;color:rgb(68,68,68);font-size:15px;background-color:rgb(255,255,255)"><br></div><div style="line-height:21.2999992370605px;color:rgb(68,68,68);font-size:15px;background-color:rgb(255,255,255)">We are trying to use Csdp to solve a programming problem.</div><div style="line-height:21.2999992370605px;color:rgb(68,68,68);font-size:15px;background-color:rgb(255,255,255)"> min trace(Sigma - X)</div><div style="line-height:21.2999992370605px;color:rgb(68,68,68);font-size:15px;background-color:rgb(255,255,255)">s.t.</div><div style="line-height:21.2999992370605px;color:rgb(68,68,68);font-size:15px;background-color:rgb(255,255,255)"> X is a diagonal matrix</div><div style="line-height:21.2999992370605px;color:rgb(68,68,68);font-size:15px;background-color:rgb(255,255,255)"> (Sigma - X ) >= 0, positive definite</div><div style="line-height:21.2999992370605px;color:rgb(68,68,68);font-size:15px;background-color:rgb(255,255,255)"><br style="line-height:21.2999992370605px"></div><div style="line-height:21.2999992370605px;color:rgb(68,68,68);font-size:15px;background-color:rgb(255,255,255)">Where Sigma is a known covariance matrix of several random variables.</div><div style="line-height:21.2999992370605px;color:rgb(68,68,68);font-size:15px;background-color:rgb(255,255,255)">We have problems when trying to add "X is a diagonal matrix" constraint.</div></div></div></blockquote><div><br></div><div>The natural way to formulate this as an SDP is </div><div> </div><div>min sum(y(i),i=1..n)</div><div> </div><div>Sigma-sum(y(i)*Eii,i=1..n) is PSD</div><div> </div><div>where Eii is an n by n zero matrix with a 1 in the (i,i) position. Once you've got a solution, your matrix is simply X=diag(y). This problem is in the dual form, but since CSDP (and other SDP solvers) produce both primal and dual solutions, you'll get the solution that you need. </div></div><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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