Symmetry in semidefinite programs

Linear Algebra and Its Applications

Volumn 430, Issue 1, 2009, Pages 360-369

  Vallentin, Frank ^a  

^a CWI   (Netherlands)

Author keywords

Binary Hamming scheme; Block diagonalization; Hahn polynomials; Semidefinite programming; Terwilliger algebra

Indexed keywords

ALGEBRA; NONLINEAR PROGRAMMING; POLYNOMIAL APPROXIMATION;

BINARY HAMMING SCHEME; BLOCK DIAGONALIZATION; HAHN POLYNOMIALS; SEMIDEFINITE PROGRAMMING; TERWILLIGER ALGEBRA;

POLYNOMIALS;

EID: 54149086891     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2008.07.025     Document Type: Article

References (20)

1. Babai L., and Rónyai L. Computing irreducible representations of finite groups. Math. Comp. 55 (1990) 705-722
2. Bachoc C., and Vallentin F. New upper bounds for kissing numbers from semidefinite programming. J. Amer. Math. Soc. 21 (2008) 909-924
3. Y. Bai, E. de Klerk, D.V. Pasechnik, R. Sotirov, Exploiting group symmetry in truss topology optimization, preprint, Optimization Online, April 2007.
4. Boyd S., Diaconis P., and Xiao L. Fastest mixing Markov chain on a graph. SIAM Rev. 46 (2004) 667-689
5. E. de Klerk, D.V. Pasechnik, Solving SDP's in non-commutative algebras part I: the dual-scaling algorithm, Discussion paper from Tilburg University, Center for Economic Research, 2005.
6. de Klerk E., Pasechnik D.V., and Schrijver A. Reduction of symmetric semidefinite programs using the regular *-representation. Math. Program. 109 (2007) 613-624
7. E. de Klerk, R. Sotirov, Exploiting group symmetry in semidefinite programming relaxations of the quadratic assignment problem, preprint, Optimization Online, June 2007.
8. Dunkl C.F. A Krawtchouk polynomial addition theorem and wreath product of symmetric groups. Indiana Univ. Math. J. 25 (1976) 335-358
9. Dunkl C.F. Spherical functions on compact groups and applications to special functions. Sympos. Math. 22 (1979) 145-161
10. Gatermann K., and Parrilo P.A. Symmetry groups, semidefinite programs, and sums of squares. J. Pure Appl. Algebra 192 (2004) 95-128
11. Gijswijt D.C., Schrijver A., and Tanaka H. New upper bounds for nonbinary codes. J. Combin. Theory Ser. A 13 (2006) 1719-1731
12. Goodman R., and Wallach N.R. Representations and Invariants of the Classical Groups (1998), Cambridge University Press
13. N. Gvozdenović, M. Laurent, Computing the ψ and Ψ semidefinite programming bounds for the chromatic number, preprint, Optimization Online, February, 2007.
14. L. Jansson, J.B. Lasserre, C. Riener, T. Theobald, Exploiting symmetries in SDP-relaxations for polynomial optimization, preprint, Optimization Online, September 2006.
15. Karlin S., and McGregor J. The Hahn polynomials, formulas and an application. Scr. Math. 26 (1961) 33-46
16. Kanno Y., Ohsaki M., Murota K., and Katoh N. Group symmetry in interior-point methods for semidefinite program. Optim. Eng. 2 (2001) 293-320
17. Lam T.Y. A First Course in Noncommutative Rings (1991), Springer
18. Laurent M. Strengthened semidefinite programming bounds for codes. Math. Program. 109 (2007) 239-261
19. Sagan B.E. The Symmetric Group, Representations, Combinatorial Algorithms, and Symmetric Functions (2001), Springer
20. Schrijver A. New code upper bounds from the Terwilliger algebra and semidefinite programming. IEEE Trans. Inform. Theory 51 (2005) 2859-2866