IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v63y2015i4p653-675.html
   My bibliography  Save this article

Interiors of completely positive cones

Author

Listed:
  • Anwa Zhou
  • Jinyan Fan

Abstract

A symmetric matrix A is completely positive (CP) if there exists an entrywise nonnegative matrix B such that $$A=BB^T$$ A = B B T . We characterize the interior of the CP cone. A semidefinite algorithm is proposed for checking whether a matrix is in the interior of the CP cone, and its properties are studied. A CP-decomposition of a matrix in Dickinson’s form can be obtained if it is an interior of the CP cone. Some computational experiments are also presented. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Anwa Zhou & Jinyan Fan, 2015. "Interiors of completely positive cones," Journal of Global Optimization, Springer, vol. 63(4), pages 653-675, December.
    • Handle: RePEc:spr:jglopt:v:63:y:2015:i:4:p:653-675
    DOI: 10.1007/s10898-015-0309-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-015-0309-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-015-0309-0?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. 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.
    2. Bomze, Immanuel M., 2012. "Copositive optimization – Recent developments and applications," European Journal of Operational Research, Elsevier, vol. 216(3), pages 509-520.
    3. Peter Dickinson & Luuk Gijben, 2014. "On the computational complexity of membership problems for the completely positive cone and its dual," Computational Optimization and Applications, Springer, vol. 57(2), pages 403-415, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jinyan Fan & Anwa Zhou, 2017. "A semidefinite algorithm for completely positive tensor decomposition," Computational Optimization and Applications, Springer, vol. 66(2), pages 267-283, March.
    2. Immanuel M. Bomze, 2018. "Building a completely positive factorization," 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. 26(2), pages 287-305, June.
    3. Jinyan Fan & Anwa Zhou, 2016. "Computing the distance between the linear matrix pencil and the completely positive cone," Computational Optimization and Applications, Springer, vol. 64(3), pages 647-670, July.

    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. Jinyan Fan & Anwa Zhou, 2016. "Computing the distance between the linear matrix pencil and the completely positive cone," Computational Optimization and Applications, Springer, vol. 64(3), pages 647-670, July.
    2. Bomze, Immanuel M. & Gabl, Markus, 2023. "Optimization under uncertainty and risk: Quadratic and copositive approaches," European Journal of Operational Research, Elsevier, vol. 310(2), pages 449-476.
    3. Jinyan Fan & Anwa Zhou, 2017. "A semidefinite algorithm for completely positive tensor decomposition," Computational Optimization and Applications, Springer, vol. 66(2), pages 267-283, March.
    4. Zhijian Lai & Akiko Yoshise, 2022. "Completely positive factorization by a Riemannian smoothing method," Computational Optimization and Applications, Springer, vol. 83(3), pages 933-966, December.
    5. Gabriele Eichfelder & Patrick Groetzner, 2022. "A note on completely positive relaxations of quadratic problems in a multiobjective framework," Journal of Global Optimization, Springer, vol. 82(3), pages 615-626, March.
    6. Peter J. C. Dickinson & Janez Povh, 2013. "Moment Approximations for Set-Semidefinite Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 57-68, October.
    7. Akihiro Tanaka & Akiko Yoshise, 2018. "LP-based tractable subcones of the semidefinite plus nonnegative cone," Annals of Operations Research, Springer, vol. 265(1), pages 155-182, June.
    8. Anwa Zhou & Jinyan Fan, 2018. "Completely positive tensor recovery with minimal nuclear value," Computational Optimization and Applications, Springer, vol. 70(2), pages 419-441, June.
    9. Peter Dickinson & Janez Povh, 2015. "On an extension of Pólya’s Positivstellensatz," Journal of Global Optimization, Springer, vol. 61(4), pages 615-625, April.
    10. Anwa Zhou & Jinyan Fan, 2019. "A hierarchy of semidefinite relaxations for completely positive tensor optimization problems," Journal of Global Optimization, Springer, vol. 75(2), pages 417-437, October.
    11. Jinyan Fan & Jiawang Nie & Anwa Zhou, 2019. "Completely Positive Binary Tensors," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 1087-1100, August.
    12. Xiao Wang & Xinzhen Zhang & Guangming Zhou, 2020. "SDP relaxation algorithms for $$\mathbf {P}(\mathbf {P}_0)$$P(P0)-tensor detection," Computational Optimization and Applications, Springer, vol. 75(3), pages 739-752, April.
    13. Laurent, Monique & Vargas, Luis Felipe, 2022. "Finite convergence of sum-of-squares hierarchies for the stability number of a graph," Other publications TiSEM 3998b864-7504-4cf4-bc1d-f, Tilburg University, School of Economics and Management.
    14. Laurent, M. & Rostalski, P., 2012. "The approach of moments for polynomial equations," Other publications TiSEM f08f3cd2-b83e-4bf1-9322-a, Tilburg University, School of Economics and Management.
    15. Tomohiko Mizutani & Makoto Yamashita, 2013. "Correlative sparsity structures and semidefinite relaxations for concave cost transportation problems with change of variables," Journal of Global Optimization, Springer, vol. 56(3), pages 1073-1100, July.
    16. Fook Wai Kong & Polyxeni-Margarita Kleniati & Berç Rustem, 2012. "Computation of Correlated Equilibrium with Global-Optimal Expected Social Welfare," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 237-261, April.
    17. Sandra S. Y. Tan & Antonios Varvitsiotis & Vincent Y. F. Tan, 2021. "Analysis of Optimization Algorithms via Sum-of-Squares," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 56-81, July.
    18. Immanuel M. Bomze & Vaithilingam Jeyakumar & Guoyin Li, 2018. "Extended trust-region problems with one or two balls: exact copositive and Lagrangian relaxations," Journal of Global Optimization, Springer, vol. 71(3), pages 551-569, July.
    19. Hao Hu & Renata Sotirov, 2021. "The linearization problem of a binary quadratic problem and its applications," Annals of Operations Research, Springer, vol. 307(1), pages 229-249, December.
    20. Yuzhu Wang & Akihiro Tanaka & Akiko Yoshise, 2021. "Polyhedral approximations of the semidefinite cone and their application," Computational Optimization and Applications, Springer, vol. 78(3), pages 893-913, April.

    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:63:y:2015:i:4:p:653-675. 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.