Symmetry reduction in convex optimization with applications in combinatorics

Daniel Brosch

Research output: ThesisDoctoral Thesis

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Abstract

This dissertation explores different approaches to and applications of symmetry reduction in convex optimization. Using tools from semidefinite programming, representation theory and algebraic combinatorics, hard combinatorial problems are solved or bounded. The first chapters consider the Jordan reduction method, extend the method to optimization over the doubly nonnegative cone, and apply it to quadratic assignment problems and energy minimization on a discrete torus. The following chapter uses symmetry reduction as a proving tool, to approach a problem from queuing theory with redundancy scheduling. The final chapters propose generalizations and reductions of flag algebras, a powerful tool for problems coming from extremal combinatorics.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Tilburg University
Supervisors/Advisors
  • de Klerk, Etienne, Promotor
  • Laurent, Monique, Promotor
Award date19 Oct 2022
Place of PublicationTilburg
Publisher
Print ISBNs978 90 5668 690 1
DOIs
Publication statusPublished - 2022

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