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On an enumerative algorithm for solving eigenvalue complementarity problems


  • Luís Fernandes


  • Joaquim Júdice


  • Hanif Sherali


  • Maria Forjaz



In this paper, we discuss the solution of linear and quadratic eigenvalue complementarity problems (EiCPs) using an enumerative algorithm of the type introduced by Júdice et al. (Optim. Methods Softw. 24:549–586, 2009 ). Procedures for computing the interval that contains all the eigenvalues of the linear EiCP are first presented. A nonlinear programming (NLP) model for the quadratic EiCP is formulated next, and a necessary and sufficient condition for a stationary point of the NLP to be a solution of the quadratic EiCP is established. An extension of the enumerative algorithm for the quadratic EiCP is also developed, which solves this problem by computing a global minimum for the NLP formulation. Some computational experience is presented to highlight the efficiency and efficacy of the proposed enumerative algorithm for solving linear and quadratic EiCPs. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • 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.
  • Handle: RePEc:spr:coopap:v:59:y:2014:i:1:p:113-134
    DOI: 10.1007/s10589-012-9529-0

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    References listed on IDEAS

    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. repec:eee:apmaco:v:271:y:2015:i:c:p:594-608 is not listed on IDEAS
    3. Carmo P. Brás & Alfredo N. Iusem & Joaquim J. Júdice, 2016. "On the quadratic eigenvalue complementarity problem," Journal of Global Optimization, Springer, vol. 66(2), pages 153-171, October.


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