{"id":148,"date":"2026-02-11T08:23:53","date_gmt":"2026-02-11T08:23:53","guid":{"rendered":"https:\/\/almoa.aau.at\/?page_id=64"},"modified":"2026-03-28T19:23:39","modified_gmt":"2026-03-28T18:23:39","slug":"dc-10-bilevel-optimisation-under-uncertainty","status":"publish","type":"page","link":"https:\/\/almoa.aau.at\/?page_id=148","title":{"rendered":"DC 10 &#8211; Bilevel optimisation under uncertainty"},"content":{"rendered":"<div class=\"dc-project\">\r\n<p class=\"wp-block-paragraph\"><strong>Project Title:<\/strong> Bilevel optimisation under uncertainty<br \/><strong>Doctoral Candidate:<\/strong> N.N.<br \/><strong>Host Institution:<\/strong>\u00a0TU Dortmund University<br \/><strong>Supervisors:<\/strong> <a href=\"https:\/\/wwwold.mathematik.tu-dortmund.de\/de\/personen\/person\/Christoph+Buchheim.html\">Christoph Buchheim<\/a>, <a href=\"https:\/\/www.lix.polytechnique.fr\/Labo\/Claudia.D'Ambrosio\/\">Claudia D\u2019Ambrosio<\/a><\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\"><strong>Objectives:<\/strong> In bilevel optimisation, it is usually assumed that the leader has perfect knowledge of the follower&#8217;s subproblem. However, this assumption is rather unrealistic. It is therefore natural to address robust or stochastic bilevel optimisation problems (or to consider more general risk measures). Not much is known about such problems, and it turns out that the situation is very different from that of single level optimisation under uncertainty. E.g., in the robust model, the adversary is not an adversary of the follower, but of the leader, which changes the algorithmic and even the typical complexity theoretic situation considerably. The first objective of the PhD project is to derive (relative) complexity results for different types of uncertainty sets or different probability distributions, which determines the types of algorithms one can hope to obtain. The second objective is to develop such (exact or approximate) algorithms, either for specific combinatorial structures or for general bilevel problems. The latter could be addressed using either oracle-based approaches or general LP or IP formulations on both levels. The resulting algorithms will be implemented and tested experimentally.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\"><strong>Expected Results:<\/strong> Complexity results for specific classes of bilevel optimisation problems under uncertainty. New algorithmic approaches for bilevel optimisation problems under uncertainty. Implementation and experimental evaluation of these approaches.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\"><strong>Planned secondment:<\/strong> 6 months at CNRS (C. D&#8217;Ambrosio), starting in the second half of the 2nd year, to implement and improve algorithms for bilevel optimisation under uncertainty; 2 months at Optit (A. Bettinelli) at the beginning of the 2nd year to gain experience with the solution of real-world optimisation problems.<\/p>\r\n\r\n\r\n\r\n<p class=\"wp-block-paragraph\"><strong>Degree awarding institution:<\/strong> TU Dortmund University<\/p>\r\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Project Title: Bilevel optimisation under uncertaintyDoctoral Candidate: N.N.Host Institution:\u00a0TU Dortmund UniversitySupervisors: Christoph Buchheim, Claudia D\u2019Ambrosio Objectives: In bilevel optimisation, it is usually assumed that the leader has perfect knowledge of the follower&#8217;s subproblem. However, this assumption is rather unrealistic. It is therefore natural to address robust or stochastic bilevel optimisation [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_crdt_document":"","footnotes":""},"class_list":["post-148","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/almoa.aau.at\/index.php?rest_route=\/wp\/v2\/pages\/148","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/almoa.aau.at\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/almoa.aau.at\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/almoa.aau.at\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/almoa.aau.at\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=148"}],"version-history":[{"count":4,"href":"https:\/\/almoa.aau.at\/index.php?rest_route=\/wp\/v2\/pages\/148\/revisions"}],"predecessor-version":[{"id":872,"href":"https:\/\/almoa.aau.at\/index.php?rest_route=\/wp\/v2\/pages\/148\/revisions\/872"}],"wp:attachment":[{"href":"https:\/\/almoa.aau.at\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=148"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}