{"id":981,"date":"2025-04-19T09:05:00","date_gmt":"2025-04-19T09:05:00","guid":{"rendered":"https:\/\/web.eecs.umich.edu\/~girasole\/?p=981"},"modified":"2025-05-19T21:06:53","modified_gmt":"2025-05-19T21:06:53","slug":"sdp-relaxation-paper-in-simax","status":"publish","type":"post","link":"https:\/\/web.eecs.umich.edu\/~girasole\/?p=981","title":{"rendered":"SDP Relaxation paper in SIMAX"},"content":{"rendered":"\n<p>I&#8217;m excited that our paper &#8220;A Semidefinite Relaxation for Sums of Heterogeneous Quadratic Forms on the Stiefel Manifold&#8221; has been published in the <em>SIAM Journal on Matrix Analysis and Applications<\/em>. <a href=\"https:\/\/doi.org\/10.1137\/23M1545136\">https:\/\/doi.org\/10.1137\/23M1545136<\/a>. We were inspired to work on this problem after it popped up inside the heteroscedastic PCA problem. It&#8217;s a fascinating, simple, general problem with connections to PCA, joint diagonalization, and low-rank semidefinite programs. Applying the standard Schur relaxation to this problem gives a trivial (and incorrect) solution, but one minor change makes the relaxation powerful and even tight in many instances. You can find the <a href=\"https:\/\/github.com\/kgilman\/Sums-of-Heterogeneous-Quadratics\">code for experiments here<\/a>. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>I&#8217;m excited that our paper &#8220;A Semidefinite Relaxation for Sums of Heterogeneous Quadratic Forms on the Stiefel Manifold&#8221; has been published in the SIAM Journal on Matrix Analysis and Applications. https:\/\/doi.org\/10.1137\/23M1545136. We were inspired to work on this problem after it popped up inside the heteroscedastic PCA problem. It&#8217;s a fascinating, simple, general problem with [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[3,4],"tags":[],"_links":{"self":[{"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/posts\/981"}],"collection":[{"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=981"}],"version-history":[{"count":1,"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/posts\/981\/revisions"}],"predecessor-version":[{"id":982,"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/posts\/981\/revisions\/982"}],"wp:attachment":[{"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=981"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=981"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=981"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}