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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

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    1. 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.
    2. 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).
    3. 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).
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    Cited by:

    1. Peter Dickinson & Janez Povh, 2015. "On an extension of Pólya’s Positivstellensatz," Journal of Global Optimization, Springer, vol. 61(4), pages 615-625, April.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Marco Locatelli, 2013. "Approximation algorithm for a class of global optimization problems," Journal of Global Optimization, Springer, vol. 55(1), pages 13-25, January.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. M. Locatelli, 2009. "Complexity Results for Some Global Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 93-102, January.
    15. 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.
    16. 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.

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