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A sequential partial linearization algorithm for the symmetric eigenvalue complementarity problem

Author

Listed:
  • Masao Fukushima

    (Nanzan University)

  • Joaquim Júdice

    (Universidade de Coimbra)

  • Welington Oliveira

    (PSL Research University, CMA Centre de Mathématiques Appliquées)

  • Valentina Sessa

    (PSL Research University, CMA Centre de Mathématiques Appliquées)

Abstract

In this paper, we introduce a Sequential Partial Linearization (SPL) algorithm for finding a solution of the symmetric Eigenvalue Complementarity Problem (EiCP). The algorithm can also be used for the computation of a stationary point of a standard fractional quadratic program. A first version of the SPL algorithm employs a line search technique and possesses global convergence to a solution of the EiCP under a simple condition related to the minimum eigenvalue of one of the matrices of the problem. Furthermore, it is shown that this condition is verified for a simpler version of the SPL algorithm that does not require a line search technique. The main computational effort of the SPL algorithm is the solution of a strictly convex standard quadratic problem, which is efficiently solved by a finitely convergent block principal pivoting algorithm. Numerical results of the solution of test problems from different sources indicate that the SPL algorithm is in general efficient for the solution of the symmetric EiCP in terms of the number of iterations, accuracy of the solution and total computational effort.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:77:y:2020:i:3:d:10.1007_s10589-020-00226-7
    DOI: 10.1007/s10589-020-00226-7
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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. 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.
    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. 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.
    5. Le An & Pham Tao, 2005. "The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems," Annals of Operations Research, Springer, vol. 133(1), pages 23-46, January.
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    Cited by:

    1. 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.

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