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Improved dc programming approaches for solving the quadratic eigenvalue complementarity problem

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  • Niu, Yi-Shuai
  • Júdice, Joaquim
  • Le Thi, Hoai An
  • Pham, Dinh Tao

Abstract

In this paper, we discuss the solution of a Quadratic Eigenvalue Complementarity Problem (QEiCP) by using Difference of Convex (DC) programming approaches. We first show that QEiCP can be represented as dc programming problem. Then we investigate different dc programming formulations of QEiCP and discuss their dc algorithms based on a well-known method – DCA. A new local dc decomposition is proposed which aims at constructing a better dc decomposition regarding to the specific feature of the target problem in some neighborhoods of the iterates. This new procedure yields faster convergence and better precision of the computed solution. Numerical results illustrate the efficiency of the new dc algorithms in practice.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:353:y:2019:i:c:p:95-113
    DOI: 10.1016/j.amc.2019.02.017
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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.
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    3. 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.
    4. 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.
    5. 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.
    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. 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.
    8. Tao Pham Dinh & Yi-Shuai Niu, 2011. "An efficient DC programming approach for portfolio decision with higher moments," Computational Optimization and Applications, Springer, vol. 50(3), pages 525-554, December.
    9. 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.
    10. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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