{"id":2977,"date":"2022-03-03T10:22:52","date_gmt":"2022-03-03T16:22:52","guid":{"rendered":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/?post_type=tribe_events&#038;p=2977"},"modified":"2022-03-18T16:13:16","modified_gmt":"2022-03-18T21:13:16","slug":"lans-seminar-28","status":"publish","type":"tribe_events","link":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/event\/lans-seminar-28\/","title":{"rendered":"LANS Seminar"},"content":{"rendered":"<p><strong>Seminar Title<\/strong>: Scalable Semidefinite and Polynomial Optimization via Matrix Decomposition<br \/>\n<strong>Speaker<\/strong>: Yang Zheng, Assistant Professor, Electrical and Computer Engineering, University of California, San Diego<\/p>\n<p><strong>Date\/Time<\/strong>: March 23, 2022 \/ 10:30 am &#8211; 11:30 am<br \/>\n<strong>Location<\/strong>: See meeting URL on the cels-seminars website\u00a0(requires Argonne login)<\/p>\n<p><strong>Host<\/strong>: Prassana Balprakash<\/p>\n<hr \/>\n<p><strong>Description<\/strong>: Semidefinite and sum-of-squares (SOS) optimization are two types of convex optimization problems, which have found a wide range of applications in control theory, fluid dynamics, machine learning, and power systems. They can be solved in polynomial-time using interior-point methods in theory, but these methods are only practical for small- to medium-sized instances. In this talk, I will introduce matrix decomposition methods for semidefinite and SOS optimization, which scale more favorably to large-scale problem instances. In the first part, I will apply chordal decomposition to reformulate a sparse semidefinite program (SDP) into an equivalent SDP with smaller PSD constraints that is suitable for the application of first-order methods. The resulting algorithms have been implemented in the open-source solver CDCS. In the second part, I will extend the classical chordal decomposition to the case of sparse polynomial matrices that are positive (semi)definite globally or locally on a semi-algebraic set. The extended decomposition results can be viewed as sparsity-exploiting versions of the Hilbert-Artin, Reznick, Putinar, and Putinar-Vasilescu Positivstellens\u00e4tze. They allow for much more efficient computations for sparse problems. This talk is based on our work:\u00a0<a href=\"https:\/\/arxiv.org\/abs\/1707.05058\">https:\/\/arxiv.org\/abs\/1707.05058<\/a>, and\u00a0<a href=\"https:\/\/arxiv.org\/abs\/2007.11410\">https:\/\/arxiv.org\/abs\/2007.11410<\/a><\/p>\n<p><em>Please note that the meeting URL for this event can be seen on the <\/em>cels-seminars website<em>, which requires an Argonne login.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Seminar Title: Scalable Semidefinite and Polynomial Optimization via Matrix Decomposition Speaker: Yang Zheng, Assistant Professor, Electrical and Computer Engineering, University of California, San Diego Date\/Time: March 23, 2022 \/ 10:30 am &#8211; 11:30 am Location: See meeting URL on the &hellip; <a href=\"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/event\/lans-seminar-28\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":43,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_tribe_events_status":"","_tribe_events_status_reason":"","footnotes":"","_members_access_role":[],"_members_access_error":""},"tags":[],"tribe_events_cat":[2],"class_list":["post-2977","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-seminar","cat_seminar"],"acf":[],"_links":{"self":[{"href":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/wp-json\/wp\/v2\/tribe_events\/2977","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/wp-json\/wp\/v2\/tribe_events"}],"about":[{"href":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/wp-json\/wp\/v2\/types\/tribe_events"}],"author":[{"embeddable":true,"href":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/wp-json\/wp\/v2\/users\/43"}],"version-history":[{"count":4,"href":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/wp-json\/wp\/v2\/tribe_events\/2977\/revisions"}],"predecessor-version":[{"id":3031,"href":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/wp-json\/wp\/v2\/tribe_events\/2977\/revisions\/3031"}],"wp:attachment":[{"href":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/wp-json\/wp\/v2\/media?parent=2977"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/wp-json\/wp\/v2\/tags?post=2977"},{"taxonomy":"tribe_events_cat","embeddable":true,"href":"https:\/\/wordpress.cels.anl.gov\/lans-seminars\/wp-json\/wp\/v2\/tribe_events_cat?post=2977"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}