IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v140y2009i1d10.1007_s10957-008-9448-5.html
   My bibliography  Save this article

Complexity Results for Some Global Optimization Problems

Author

Listed:
  • M. Locatelli

    (Università di Torino)

Abstract

We discuss the complexity of a class of highly structured global optimization problems, namely the maximization of separable functions, with each one-dimensional component convex and nondecreasing, over polytopes defined by a 0-1 constraint matrix with at most two variables involved in each constraint. In particular, we prove some inapproximability and approximability results.

Suggested Citation

  • M. Locatelli, 2009. "Complexity Results for Some Global Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 93-102, January.
    • Handle: RePEc:spr:joptap:v:140:y:2009:i:1:d:10.1007_s10957-008-9448-5
    DOI: 10.1007/s10957-008-9448-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-008-9448-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-008-9448-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. de Klerk, E., 2006. "The Complexity of Optimizing over a Simplex, Hypercube or Sphere : A Short Survey," Discussion Paper 2006-85, Tilburg University, Center for Economic Research.
    2. 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.
    3. de Klerk, E., 2006. "The Complexity of Optimizing over a Simplex, Hypercube or Sphere : A Short Survey," Other publications TiSEM 88640b6d-5240-472d-8669-4, Tilburg University, School of Economics and Management.
    4. 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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    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. 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. Marco Locatelli, 2013. "Approximation algorithm for a class of global optimization problems," Journal of Global Optimization, Springer, vol. 55(1), pages 13-25, January.
    5. de Klerk, E., 2006. "The Complexity of Optimizing over a Simplex, Hypercube or Sphere : A Short Survey," Discussion Paper 2006-85, Tilburg University, Center for Economic Research.
    6. de Klerk, E. & Pasechnik, D.V., 2005. "A Linear Programming Reformulation of the Standard Quadratic Optimization Problem," Other publications TiSEM f63bfe23-904e-4d7a-8677-8, Tilburg University, School of Economics and Management.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Maziar Salahi, 2010. "Convex optimization approach to a single quadratically constrained quadratic minimization problem," 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. 18(2), pages 181-187, June.
    13. 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.
    14. de Klerk, E. & Pasechnik, D.V., 2005. "A Linear Programming Reformulation of the Standard Quadratic Optimization Problem," Discussion Paper 2005-24, Tilburg University, Center for Economic Research.
    15. Andrea Cristofari & Marianna Santis & Stefano Lucidi & Francesco Rinaldi, 2020. "An active-set algorithmic framework for non-convex optimization problems over the simplex," Computational Optimization and Applications, Springer, vol. 77(1), pages 57-89, September.
    16. 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.
    17. Lek-Heng Lim, 2017. "Self-concordance is NP-hard," Journal of Global Optimization, Springer, vol. 68(2), pages 357-366, June.
    18. 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.
    19. Christoph Buchheim & Marcia Fampa & Orlando Sarmiento, 2021. "Lower Bounds for Cubic Optimization over the Sphere," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 823-846, March.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:140:y:2009:i:1:d:10.1007_s10957-008-9448-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.