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Error bounds for some semidefinite programming approaches to polynomial minimization on the hypercube

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  • de Klerk, E.

    (Tilburg University, School of Economics and Management)

  • Laurent, M.

    (Tilburg University, School of Economics and Management)

Abstract

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Suggested Citation

  • de Klerk, E. & Laurent, M., 2010. "Error bounds for some semidefinite programming approaches to polynomial minimization on the hypercube," Other publications TiSEM 619d9658-77df-4b5e-9868-0, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:619d9658-77df-4b5e-9868-09aca0615347
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    File URL: https://pure.uvt.nl/ws/portalfiles/portal/1270971/hypercube_approx_paper_ML5-1_SIAMstyle.pdf
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    References listed on IDEAS

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    1. de Klerk, E. & Laurent, M. & Parrilo, P., 2006. "A PTAS for the minimization of polynomials of fixed degree over the simplex," Other publications TiSEM 603897c9-179e-43e4-9e83-6, Tilburg University, School of Economics and Management.
    2. Laurent, M., 2009. "Sums of squares, moment matrices and optimization over polynomials," Other publications TiSEM 9fef820b-69d2-43f2-a501-e, Tilburg University, School of Economics and Management.
    3. de Klerk, E., 2008. "The complexity of optimizing over a simplex, hypercube or sphere : A short survey," Other publications TiSEM 485b6860-cf1d-4cad-97b8-2, Tilburg University, School of Economics and Management.
    4. Etienne Klerk, 2008. "The complexity of optimizing over a simplex, hypercube or sphere: a short survey," 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. 16(2), pages 111-125, June.
    5. Jean B. Lasserre, 2002. "Semidefinite Programming vs. LP Relaxations for Polynomial Programming," Mathematics of Operations Research, INFORMS, vol. 27(2), pages 347-360, May.
    6. NESTEROV, Yu. & WOLKOWICZ, Henry & YE, Yinyu, 2000. "Semidefinite programming relaxations of nonconvex quadratic optimization," LIDAM Reprints CORE 1471, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. de Klerk, Etienne & Laurent, Monique, 2018. "Worst-case examples for Lasserre's measure-based hierarchy for polynomial optimization on the hypercube," Other publications TiSEM a939e3b3-0361-42c9-8263-0, Tilburg University, School of Economics and Management.
    2. de Klerk, Etienne & Laurent, Monique, 2019. "A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis," Other publications TiSEM d956492f-3e25-4dda-a5e2-e, Tilburg University, School of Economics and Management.
    3. Kirschner, Felix & de Klerk, Etienne, 2023. "Construction of multivariate polynomial approximation kernels via semidefinite programming," Other publications TiSEM 9b1d01ec-074f-404f-a8d0-6, Tilburg University, School of Economics and Management.
    4. Monique Laurent & Zhao Sun, 2014. "Handelman’s hierarchy for the maximum stable set problem," Journal of Global Optimization, Springer, vol. 60(3), pages 393-423, November.
    5. Myoung-Ju Park & Sung-Pil Hong, 2013. "Handelman rank of zero-diagonal quadratic programs over a hypercube and its applications," Journal of Global Optimization, Springer, vol. 56(2), pages 727-736, June.
    6. Etienne de Klerk & Monique Laurent, 2020. "Worst-Case Examples for Lasserre’s Measure–Based Hierarchy for Polynomial Optimization on the Hypercube," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 86-98, February.
    7. Etienne de Klerk & Jean B. Lasserre & Monique Laurent & Zhao Sun, 2017. "Bound-Constrained Polynomial Optimization Using Only Elementary Calculations," Mathematics of Operations Research, INFORMS, vol. 42(3), pages 834-853, August.

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