2026-07-24T11:54:14Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:13646 2024-03-06T10:52:33Z ddc:004 open_access

Optimization, Complexity and Invariant Theory (Invited Talk) Bürgisser, Peter geometric invariant theory geodesic optimization non-commutative optimization null cone operator scaling moment polytope orbit closure intersection geometric programming Invariant and representation theory studies symmetries by means of group actions and is a well established source of unifying principles in mathematics and physics. Recent research suggests its relevance for complexity and optimization through quantitative and algorithmic questions. The goal of the talk is to give an introduction to new algorithmic and analysis techniques that extend convex optimization from the classical Euclidean setting to a general geodesic setting. We also point out surprising connections to a diverse set of problems in different areas of mathematics, statistics, computer science, and physics. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Peter Bürgisser 2021 Is Part Of LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2021.1 urn:nbn:de:0030-drops-136460 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.1 eng https://creativecommons.org/licenses/by/4.0/legalcode