License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2021.1
URN: urn:nbn:de:0030-drops-136460
URL: https://drops.dagstuhl.de/opus/volltexte/2021/13646/
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B├╝rgisser, Peter

Optimization, Complexity and Invariant Theory (Invited Talk)

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LIPIcs-STACS-2021-1.pdf (0.8 MB)


Abstract

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.

BibTeX - Entry

@InProceedings{burgisser:LIPIcs.STACS.2021.1,
  author =	{B\"{u}rgisser, Peter},
  title =	{{Optimization, Complexity and Invariant Theory}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{1:1--1:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/13646},
  URN =		{urn:nbn:de:0030-drops-136460},
  doi =		{10.4230/LIPIcs.STACS.2021.1},
  annote =	{Keywords: geometric invariant theory, geodesic optimization, non-commutative optimization, null cone, operator scaling, moment polytope, orbit closure intersection, geometric programming}
}

Keywords: geometric invariant theory, geodesic optimization, non-commutative optimization, null cone, operator scaling, moment polytope, orbit closure intersection, geometric programming
Collection: 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)
Issue Date: 2021
Date of publication: 10.03.2021


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