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On the solution of the symmetric eigenvalue complementarity problem by the spectral projected gradient algorithm

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Abstract

This paper is devoted to the eigenvalue complementarity problem (EiCP) with symmetric real matrices. This problem is equivalent to finding a stationary point of a differentiable optimization program involving the Rayleigh quotient on a simplex (Queiroz et al., Math. Comput. 73, 1849–1863, 2004). We discuss a logarithmic function and a quadratic programming formulation to find a complementarity eigenvalue by computing a stationary point of an appropriate merit function on a special convex set. A variant of the spectral projected gradient algorithm with a specially designed line search is introduced to solve the EiCP. Computational experience shows that the application of this algorithm to the logarithmic function formulation is a quite efficient way to find a solution to the symmetric EiCP.

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Authors and Affiliations

  1. Dpto. de Matemática, Universidade de Coimbra, Coimbra, Portugal

    Joaquim J. Júdice

  2. Dpto. de Computación, Universidad Central de Venezuela, Ap. 47002, Caracas, 1041-A, Venezuela

    Marcos Raydan

  3. Dpto. de Matemática, Universidade da Beira Interior, Covilhã, Portugal

    Silvério S. Rosa

  4. Dpto. de Matemática Aplicada, IMECC-UNICAMP, CP 6065, 13081-970, Campinas, SP, Brazil

    Sandra A. Santos

Authors
  1. Joaquim J. Júdice
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  2. Marcos Raydan
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  3. Silvério S. Rosa
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  4. Sandra A. Santos
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Correspondence to Marcos Raydan.

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Júdice, J.J., Raydan, M., Rosa, S.S. et al. On the solution of the symmetric eigenvalue complementarity problem by the spectral projected gradient algorithm. Numer Algor 47, 391–407 (2008). https://doi.org/10.1007/s11075-008-9194-7

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  • DOI: https://doi.org/10.1007/s11075-008-9194-7

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