{"id":6241,"date":"2020-10-26T16:47:39","date_gmt":"2020-10-26T15:47:39","guid":{"rendered":"http:\/\/www.mi.uni-koeln.de\/opt\/?page_id=6241"},"modified":"2021-02-06T17:37:15","modified_gmt":"2021-02-06T16:37:15","slug":"konvexe-optimierung-ws-2020-21","status":"publish","type":"page","link":"http:\/\/www.mi.uni-koeln.de\/opt\/veranstaltungen\/konvexe-optimierung-ws-2020-21\/","title":{"rendered":"Konvexe Optimierung (WS 2020\/21)"},"content":{"rendered":"\n

Lecturer<\/strong>
Prof. Dr. Frank Vallentin<\/a><\/p>\n\n\n\n

Coordination of the Exercise Sessions<\/strong>
Dr. Marc Zimmermann, Greta Fischer<\/p>\n\n\n\n

Sprache\/Language<\/strong>
\u00dcbungsaufgaben und die Abschlussklausur k\u00f6nnen wahlweise in Englisch oder in Deutsch bearbeitet werden.
The course will be organized in English. Exercises and the final exam can be submitted either in German or in English.<\/p>\n\n\n\n

Contents
<\/strong>In modern „Convex Optimization“ the theory of semidefinite optimization plays a central role. Semidefinite optimization is a generalization of linear optimization, where one wants to optimize linear functions over positive semidefinite matrices restricted by linear constraints. A wide class of convex optimization problems can be modeled using semidefinite optimization. On the one hand, there are algorithms to solve semidefinite optimization problems, which are efficient in theory and practice. On the other hand, semidefinite optimization is a tool of particular usefulness and elegance.<\/p>\n\n\n\n

The aim of this course is to provide an introduction to the theory of semidefinite optimization, to algorithmic techniques, and to mathematical applications in combinatorics, geometry and algebra.<\/p>\n\n\n\n

Literature \/ Extended lecture notes<\/strong>
[ddownload id=“6265″ text=“Monique Laurent, Frank Vallentin –  A Course on Semidefinite Optimization (updated: January 4, 2021)“]<\/p>\n\n\n\n

Week plan<\/strong><\/p>\n\n\n\n

  1. Week (3.11.): Introduction and convexity recap (Appendix A)<\/li>
  2. Week (10.11.): Conic optimization (Chapter 2)<\/li>
  3. Week (17.11.): The cone of positive semidefinite matrices (Appendix B)<\/li>
  4. Week (24.11.): No lecture<\/strong> (due to move of the group)<\/li>
  5. Week (1.12.): Eigenvalue optimization and convex spectral functions (Chapter 1.2, Chapter 1.3, Chapter 7.1)<\/li>
  6. Week (8.12.): Optimization with ellipsoids (Chapter 7.2, Chapter 7.3)<\/li>
  7. Week (15.12.): The ellipsoid method (Chapter 3)<\/li>
  8. Week (12.1): Approximating MAXCUT (Chapter 5.1, Chapter 5.2, Chapter 5.3.1, Chapter 5.3.2)<\/li>
  9. Week (19.1.): Grothendieck inequalities (Chapter 5.3.5, Chapter 6.2)<\/li>
  10. Week (26.1.): Graph coloring and independent sets (Chapter 4.1.1, Chapter 4.3.1, Chapter 4.4.1, Chapter 4.6)<\/li>
  11. Week (2.2.): Packings on the sphere (Chapter 10.1, Chapter 10.2, Chapter 10.3, Chapter 10.5, Chapter 10.6)<\/li>
  12. Week (9.2.): Examination week<\/li><\/ol>\n\n\n\n

    Lectures<\/strong>
    Tuesday 8.15-9.45 (zoom)
    Friday 8.15-9.45 (zoom)<\/p>\n\n\n\n

    Exercise Sessions<\/strong>
    Monday 8.00-9.30 (zoom) or 14.00-15.30 (zoom)<\/p>\n\n\n\n

    Exercises<\/strong>
    \n\n\n\n\t\n\t\n\t\n\t
    [ddownload id=\"6263\" text=\"Sheet 1\"]<\/td>[ddownload id=\"6277\" text=\"Sheet 2\"] <\/td>[ddownload id=\"6286\" text=\"Sheet 3\"]<\/td>\n<\/tr>\n
    [ddownload id=\"6290\" text=\"Sheet 4\"]<\/td>[ddownload id=\"6301\" text=\"Sheet 5\"]<\/td>[ddownload id=\"6319\" text=\"Sheet 6\"] (Abgabe: 8.1.2021)<\/td>\n<\/tr>\n
    [ddownload id=\"6327\" text=\"Sheet 7\"]<\/td>[ddownload id=\"6332\" text=\"Sheet 8\"]<\/td>[ddownload id=\"6340\" text=\"Sheet 9\"]<\/td>\n<\/tr>\n
    [ddownload id=\"6342\" text=\"Sheet 10\"]<\/td><\/td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/p>\n\n\n\n

    Forum<\/strong>
    speakup<\/a><\/p>\n\n\n\n

    [ddownload id=“6353″ text=“Fragenliste zur Vorbereitung auf die m\u00fcndliche Pr\u00fcfung“]<\/p>\n","protected":false},"excerpt":{"rendered":"

    LecturerProf. Dr. Frank Vallentin Coordination of the Exercise SessionsDr. Marc Zimmermann, Greta Fischer Sprache\/Language\u00dcbungsaufgaben und die Abschlussklausur k\u00f6nnen wahlweise in Englisch oder in Deutsch bearbeitet werden.The course will be organized in English. Exercises and the final exam can be submitted either in German or in English. ContentsIn modern „Convex Optimization“ the theory of semidefinite optimization … „Konvexe Optimierung (WS 2020\/21)“ <\/span>weiterlesen<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"parent":25,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-6241","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/www.mi.uni-koeln.de\/opt\/wp-json\/wp\/v2\/pages\/6241","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.mi.uni-koeln.de\/opt\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/www.mi.uni-koeln.de\/opt\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/www.mi.uni-koeln.de\/opt\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"http:\/\/www.mi.uni-koeln.de\/opt\/wp-json\/wp\/v2\/comments?post=6241"}],"version-history":[{"count":20,"href":"http:\/\/www.mi.uni-koeln.de\/opt\/wp-json\/wp\/v2\/pages\/6241\/revisions"}],"predecessor-version":[{"id":6367,"href":"http:\/\/www.mi.uni-koeln.de\/opt\/wp-json\/wp\/v2\/pages\/6241\/revisions\/6367"}],"up":[{"embeddable":true,"href":"http:\/\/www.mi.uni-koeln.de\/opt\/wp-json\/wp\/v2\/pages\/25"}],"wp:attachment":[{"href":"http:\/\/www.mi.uni-koeln.de\/opt\/wp-json\/wp\/v2\/media?parent=6241"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}