IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v312y2017icp134-148.html
   My bibliography  Save this article

Complementarity eigenvalue problems for nonlinear matrix pencils

Author

Listed:
  • Pinto da Costa, A.
  • Seeger, A.
  • Simões, F.M.F.

Abstract

This work deals with a class of nonlinear complementarity eigenvalue problems that, from a mathematical point of view, can be written as an equilibrium model [A(λ)B(λ)C(λ)D(λ)][uw]=[v0],u≥0,v≥0,uTv=0,where the vectors u and v are subject to complementarity constraints. The block structured matrix appearing in this partially constrained equilibrium model depends continuously on a real scalar λ ∈ Λ. Such a scalar plays the role of a non-dimensional load parameter, but it may have also other physical meanings. The symbol Λ stands for a given bounded interval, possibly non-closed. The numerical problem at hand is to find all the values of λ (and, in particular, the smallest one) for which the above equilibrium model admits a nontrivial solution. By using the so-called Facial Reduction Technique, we solve efficiently such a numerical problem in various randomly generated test examples and in two mechanical examples of unilateral buckling of columns.

Suggested Citation

  • Pinto da Costa, A. & Seeger, A. & Simões, F.M.F., 2017. "Complementarity eigenvalue problems for nonlinear matrix pencils," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 134-148.
  • Handle: RePEc:eee:apmaco:v:312:y:2017:i:c:p:134-148
    DOI: 10.1016/j.amc.2017.05.028
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317303260
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2017.05.028?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. Samir Adly & Hadia Rammal, 2013. "A new method for solving Pareto eigenvalue complementarity problems," Computational Optimization and Applications, Springer, vol. 55(3), pages 703-731, July.
    2. A. Pinto da Costa & A. Seeger, 2010. "Cone-constrained eigenvalue problems: theory and algorithms," Computational Optimization and Applications, Springer, vol. 45(1), pages 25-57, January.
    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. Niu, Yi-Shuai & Júdice, Joaquim & Le Thi, Hoai An & Pham, Dinh Tao, 2019. "Improved dc programming approaches for solving the quadratic eigenvalue complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 95-113.

    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. Chen Ling & Hongjin He & Liqun Qi, 2016. "On the cone eigenvalue complementarity problem for higher-order tensors," Computational Optimization and Applications, Springer, vol. 63(1), pages 143-168, January.
    2. Fatemeh Abdi & Fatemeh Shakeri, 2017. "A New Descent Method for Symmetric Non-monotone Variational Inequalities with Application to Eigenvalue Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 923-940, June.
    3. Chen Ling & Hongjin He & Liqun Qi, 2016. "Higher-degree eigenvalue complementarity problems for tensors," Computational Optimization and Applications, Springer, vol. 64(1), pages 149-176, May.
    4. Niu, Yi-Shuai & Júdice, Joaquim & Le Thi, Hoai An & Pham, Dinh Tao, 2019. "Improved dc programming approaches for solving the quadratic eigenvalue complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 95-113.
    5. Immanuel Bomze & Werner Schachinger & Gabriele Uchida, 2012. "Think co(mpletely)positive ! Matrix properties, examples and a clustered bibliography on copositive optimization," Journal of Global Optimization, Springer, vol. 52(3), pages 423-445, March.
    6. Brás, Carmo P. & Fukushima, Masao & Iusem, Alfredo N. & Júdice, Joaquim J., 2015. "On the Quadratic Eigenvalue Complementarity Problem over a general convex cone," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 594-608.
    7. Carmo P. Brás & Joaquim J. Júdice & Hanif D. Sherali, 2014. "On the Solution of the Inverse Eigenvalue Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 162(1), pages 88-106, July.
    8. Luís Fernandes & Joaquim Júdice & Hanif Sherali & Masao Fukushima, 2014. "On the computation of all eigenvalues for the eigenvalue complementarity problem," Journal of Global Optimization, Springer, vol. 59(2), pages 307-326, July.
    9. Chuangchuang Sun, 2023. "A Customized ADMM Approach for Large-Scale Nonconvex Semidefinite Programming," Mathematics, MDPI, vol. 11(21), pages 1-27, October.
    10. Masao Fukushima & Joaquim Júdice & Welington Oliveira & Valentina Sessa, 2020. "A sequential partial linearization algorithm for the symmetric eigenvalue complementarity problem," Computational Optimization and Applications, Springer, vol. 77(3), pages 711-728, December.
    11. Pedro Gajardo & Alberto Seeger, 2012. "Reconstructing a matrix from a partial sampling of Pareto eigenvalues," Computational Optimization and Applications, Springer, vol. 51(3), pages 1119-1135, April.
    12. Bomze, Immanuel M., 2012. "Copositive optimization – Recent developments and applications," European Journal of Operational Research, Elsevier, vol. 216(3), pages 509-520.
    13. Samir Adly & Hadia Rammal, 2015. "A New Method for Solving Second-Order Cone Eigenvalue Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 563-585, May.
    14. Brás, Carmo P. & Fischer, Andreas & Júdice, Joaquim J. & Schönefeld, Klaus & Seifert, Sarah, 2017. "A block active set algorithm with spectral choice line search for the symmetric eigenvalue complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 36-48.
    15. Luís Fernandes & Joaquim Júdice & Hanif Sherali & Maria Forjaz, 2014. "On an enumerative algorithm for solving eigenvalue complementarity problems," Computational Optimization and Applications, Springer, vol. 59(1), pages 113-134, October.

    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:eee:apmaco:v:312:y:2017:i:c:p:134-148. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.