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On the computation of all eigenvalues for the eigenvalue complementarity problem

Author

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  • Luís Fernandes
  • Joaquim Júdice
  • Hanif Sherali
  • Masao Fukushima

Abstract

In this paper, a parametric algorithm is introduced for computing all eigenvalues for two Eigenvalue Complementarity Problems discussed in the literature. The algorithm searches a finite number of nested intervals $$[\bar{l}, \bar{u}]$$ [ l ¯ , u ¯ ] in such a way that, in each iteration, either an eigenvalue is computed in $$[\bar{l}, \bar{u}]$$ [ l ¯ , u ¯ ] or a certificate of nonexistence of an eigenvalue in $$[\bar{l}, \bar{u}]$$ [ l ¯ , u ¯ ] is provided. A hybrid method that combines an enumerative method [ 1 ] and a semi-smooth algorithm [ 2 ] is discussed for dealing with the Eigenvalue Complementarity Problem over an interval $$[\bar{l}, \bar{u}]$$ [ l ¯ , u ¯ ] . Computational experience is presented to illustrate the efficacy and efficiency of the proposed techniques. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:59:y:2014:i:2:p:307-326
    DOI: 10.1007/s10898-014-0165-3
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    References listed on IDEAS

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    1. Hoai Le Thi & Mahdi Moeini & Tao Pham Dinh & Joaquim Judice, 2012. "A DC programming approach for solving the symmetric Eigenvalue Complementarity Problem," Computational Optimization and Applications, Springer, vol. 51(3), pages 1097-1117, April.
    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.
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    Cited by:

    1. 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.
    2. Joaquim Júdice & Valentina Sessa & Masao Fukushima, 2022. "Solution of Fractional Quadratic Programs on the Simplex and Application to the Eigenvalue Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 545-573, June.
    3. 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.
    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.

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