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Invariant Semidefinite Programs

In: Handbook on Semidefinite, Conic and Polynomial Optimization

Author

Listed:
  • Christine Bachoc

    (Université Bordeaux I)

  • Dion C. Gijswijt

    (Leiden University
    Centrum voor Wiskunde en Informatica (CWI))

  • Alexander Schrijver

    (Centrum voor Wiskunde en Informatica (CWI)
    University of Amsterdam)

  • Frank Vallentin

    (Technical University of Delft)

Abstract

This chapter provides the reader with the necessary background for dealing with semidefinite programs which have symmetry. The basic theory is given and it is illustrated in applications from coding theory, combinatorics, geometry, and polynomial optimization.

Suggested Citation

  • Christine Bachoc & Dion C. Gijswijt & Alexander Schrijver & Frank Vallentin, 2012. "Invariant Semidefinite Programs," International Series in Operations Research & Management Science, in: Miguel F. Anjos & Jean B. Lasserre (ed.), Handbook on Semidefinite, Conic and Polynomial Optimization, chapter 0, pages 219-269, Springer.
    • Handle: RePEc:spr:isochp:978-1-4614-0769-0_9
    DOI: 10.1007/978-1-4614-0769-0_9
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    Citations

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    Cited by:

    1. Cordian Riener & Thorsten Theobald & Lina Jansson Andrén & Jean B. Lasserre, 2013. "Exploiting Symmetries in SDP-Relaxations for Polynomial Optimization," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 122-141, February.
    2. Hu, Hao & Sotirov, Renata & Wolkowicz, Henry, 2023. "Facial reduction for symmetry reduced semidefinite and doubly nonnegative programs," Other publications TiSEM 8dd3dbae-58fd-4238-b786-e, Tilburg University, School of Economics and Management.
    3. E. de Klerk & R. Sotirov & U. Truetsch, 2015. "A New Semidefinite Programming Relaxation for the Quadratic Assignment Problem and Its Computational Perspectives," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 378-391, May.
    4. Brosch, Daniel & de Klerk, Etienne, 2021. "Jordan symmetry reduction for conic optimization over the doubly nonnegative cone: Theory and software," Other publications TiSEM 283da78a-b42f-47b4-b2b7-2, Tilburg University, School of Economics and Management.
    5. Kristijan Cafuta, 2019. "Sums of Hermitian squares decomposition of non-commutative polynomials in non-symmetric variables using NCSOStools," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(2), pages 397-413, June.

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