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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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  • 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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    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. 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.
    3. 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.
    4. 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.
    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).
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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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