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Complementarity eigenvalue problems for nonlinear matrix pencils

Author

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  • Pinto da Costa, A.
  • Seeger, A.
  • Simões, F.M.F.

Abstract

This work deals with a class of nonlinear complementarity eigenvalue problems that, from a mathematical point of view, can be written as an equilibrium model [A(λ)B(λ)C(λ)D(λ)][uw]=[v0],u≥0,v≥0,uTv=0,where the vectors u and v are subject to complementarity constraints. The block structured matrix appearing in this partially constrained equilibrium model depends continuously on a real scalar λ ∈ Λ. Such a scalar plays the role of a non-dimensional load parameter, but it may have also other physical meanings. The symbol Λ stands for a given bounded interval, possibly non-closed. The numerical problem at hand is to find all the values of λ (and, in particular, the smallest one) for which the above equilibrium model admits a nontrivial solution. By using the so-called Facial Reduction Technique, we solve efficiently such a numerical problem in various randomly generated test examples and in two mechanical examples of unilateral buckling of columns.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:312:y:2017:i:c:p:134-148
    DOI: 10.1016/j.amc.2017.05.028
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    References listed on IDEAS

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    1. Samir Adly & Hadia Rammal, 2013. "A new method for solving Pareto eigenvalue complementarity problems," Computational Optimization and Applications, Springer, vol. 55(3), pages 703-731, July.
    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. 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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