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A PTAS for the minimization of polynomials of fixed degree over the simplex

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  • de Klerk, E.

    (Tilburg University, School of Economics and Management)

  • Laurent, M.

    (Tilburg University, School of Economics and Management)

  • Parrilo, P.

Abstract

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Suggested Citation

  • 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.
    • Handle: RePEc:tiu:tiutis:603897c9-179e-43e4-9e83-6a9e3e89c766
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    File URL: https://pure.uvt.nl/ws/portalfiles/portal/789265/PTAS.pdf
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    References listed on IDEAS

    as
    1. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions," LIDAM Reprints CORE 341, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. de Klerk, E. & Laurent, M. & Parrilo, P., 2005. "On the equivalence of algebraic approaches to the minimization of forms on the simplex," Other publications TiSEM 894d686e-2a57-43b2-b03a-a, Tilburg University, School of Economics and Management.
    3. NESTEROV, Yu, 2003. "Random walk in a simplex and quadratic optimization over convex polytopes," LIDAM Discussion Papers CORE 2003071, 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. Qingsong Tang & Xiangde Zhang & Guoren Wang & Cheng Zhao, 2018. "A continuous characterization of the maximum vertex-weighted clique in hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 35(4), pages 1250-1260, May.
    2. Peter Dickinson & Janez Povh, 2015. "On an extension of Pólya’s Positivstellensatz," Journal of Global Optimization, Springer, vol. 61(4), pages 615-625, April.
    3. 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.
    4. Ke Hou & Anthony Man-Cho So, 2014. "Hardness and Approximation Results for L p -Ball Constrained Homogeneous Polynomial Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1084-1108, November.
    5. 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.
    6. M. Locatelli, 2009. "Complexity Results for Some Global Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 93-102, January.
    7. Immanuel Bomze & Stefan Gollowitzer & E. Yıldırım, 2014. "Rounding on the standard simplex: regular grids for global optimization," Journal of Global Optimization, Springer, vol. 59(2), pages 243-258, July.
    8. de Klerk, E. & den Hertog, D. & Elabwabi, G., 2008. "On the complexity of optimization over the standard simplex," European Journal of Operational Research, Elsevier, vol. 191(3), pages 773-785, December.
    9. 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.
    10. Marco Locatelli, 2013. "Approximation algorithm for a class of global optimization problems," Journal of Global Optimization, Springer, vol. 55(1), pages 13-25, January.
    11. Burgdorf, S. & Laurent, Monique & Piovesan, Teresa, 2017. "On the closure of the completely positive semidefinite cone and linear approximations to quantum colorings," Other publications TiSEM fabb1d61-6395-4123-9174-b, Tilburg University, School of Economics and Management.
    12. Muhammad Faisal Iqbal & Faizan Ahmed, 2022. "Approximation Hierarchies for the Copositive Tensor Cone and Their Application to the Polynomial Optimization over the Simplex," Mathematics, MDPI, vol. 10(10), pages 1-17, May.
    13. Amir Ali Ahmadi & Georgina Hall, 2019. "On the Construction of Converging Hierarchies for Polynomial Optimization Based on Certificates of Global Positivity," Management Science, INFORMS, vol. 44(4), pages 1192-1207, November.
    14. 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.
    15. Jesús A. De Loera & Raymond Hemmecke & Matthias Köppe & Robert Weismantel, 2006. "Integer Polynomial Optimization in Fixed Dimension," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 147-153, February.
    16. Guy Kindler & Assaf Naor & Gideon Schechtman, 2010. "The UGC Hardness Threshold of the L p Grothendieck Problem," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 267-283, May.

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