Symmetry in semidefinite programs

2007/06/30 by Frank Vallentin · 1 citation
Mathematics · #math.OC #math.CO #msc:90C22 #msc:33C90

paper · pdf · doi:10.1016/j.laa.2008.07.025

published as Linear Algebra and Appl. 430 (2009), 360-369 · 10 pages (v3) minor changes, to appear in Linear Algebra and Its Applications

arxiv created 2008/07/30 · arxiv updated 2009/12/01

Abstract

This paper is a tutorial in a general and explicit procedure to simplify semidefinite programs which are invariant under the action of a symmetry group. The procedure is based on basic notions of representation theory of finite groups. As an example we derive the block diagonalization of the Terwilliger algebra of the binary Hamming scheme in this framework. Here its connection to the orthogonal Hahn and Krawtchouk polynomials becomes visible.

Cited by

• P-polynomial coherent configurations

Related

• Symmetry groups, semidefinite programs, and sums of squares
• Semidefinite programming for permutation codes
• Symmetric chains, Gelfand-Tsetlin chains, and the Terwilliger algebra of the binary Hamming scheme
• Symmetries in Linear and Integer Programs
• Block diagonalization for algebra's associated with block codes