IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v56y2013i2p727-736.html
   My bibliography  Save this article

Handelman rank of zero-diagonal quadratic programs over a hypercube and its applications

Author

Listed:
  • Myoung-Ju Park
  • Sung-Pil Hong

Abstract

It has been observed that the Handelman’s certificate of positivity of a polynomial over a compact polyhedron offers a hierarchical relaxation scheme for polynomial programs. The Handelman hierarchy seems particularly suitable for a class of combinatorial optimizations that are formulated as a zero-diagonal quadratic program over a hypercube. In this paper, we present an error analysis of Handelman hierarchy applied to the special class of polynomial programs and its implications in the computation of the combinatorial optimization problems. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:2:p:727-736
    DOI: 10.1007/s10898-012-9906-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-012-9906-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-012-9906-3?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. Kevin K. H. Cheung, 2007. "Computation of the Lasserre Ranks of Some Polytopes," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 88-94, February.
    2. 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.
    3. William Cook & Sanjeeb Dash, 2001. "On the Matrix-Cut Rank of Polyhedra," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 19-30, February.
    4. Jean B. Lasserre, 2002. "Semidefinite Programming vs. LP Relaxations for Polynomial Programming," Mathematics of Operations Research, INFORMS, vol. 27(2), pages 347-360, May.
    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. Pratik Worah, 2015. "Rank bounds for a hierarchy of Lovász and Schrijver," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 689-709, October.
    2. Monique Laurent, 2003. "A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0--1 Programming," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 470-496, August.
    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. 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. 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.
    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. Jean Lasserre & Tung Thanh, 2012. "A “joint + marginal” heuristic for 0/1 programs," Journal of Global Optimization, Springer, vol. 54(4), pages 729-744, December.
    8. de Klerk, E. & Pasechnik, D.V., 2007. "A linear programming reformulation of the standard quadratic optimization problem," Other publications TiSEM c3e74115-b343-4a85-976b-8, Tilburg University, School of Economics and Management.
    9. 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.
    10. Hanif Sherali & Evrim Dalkiran & Jitamitra Desai, 2012. "Enhancing RLT-based relaxations for polynomial programming problems via a new class of v-semidefinite cuts," Computational Optimization and Applications, Springer, vol. 52(2), pages 483-506, June.
    11. Adam Kurpisz & Samuli Leppänen & Monaldo Mastrolilli, 2017. "On the Hardest Problem Formulations for the 0/1 Lasserre Hierarchy," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 135-143, January.
    12. Gábor Braun & Samuel Fiorini & Sebastian Pokutta & David Steurer, 2015. "Approximation Limits of Linear Programs (Beyond Hierarchies)," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 756-772, March.
    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. Monique Laurent, 2003. "Lower Bound for the Number of Iterations in Semidefinite Hierarchies for the Cut Polytope," Mathematics of Operations Research, INFORMS, vol. 28(4), pages 871-883, November.
    15. Sanjeeb Dash, 2005. "Exponential Lower Bounds on the Lengths of Some Classes of Branch-and-Cut Proofs," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 678-700, August.
    16. de Klerk, Etienne & Pasechnik, Dmitrii V., 2004. "Products of positive forms, linear matrix inequalities, and Hilbert 17th problem for ternary forms," European Journal of Operational Research, Elsevier, vol. 157(1), pages 39-45, August.
    17. 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.
    18. Kevin K. H. Cheung, 2007. "Computation of the Lasserre Ranks of Some Polytopes," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 88-94, February.
    19. Warren Adams & Hanif Sherali, 2005. "A Hierarchy of Relaxations Leading to the Convex Hull Representation for General Discrete Optimization Problems," Annals of Operations Research, Springer, vol. 140(1), pages 21-47, November.
    20. 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.

    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:jglopt:v:56:y:2013:i:2:p:727-736. 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.