Abstract
In this paper, a parametric algorithm is introduced for computing all eigenvalues for two Eigenvalue Complementarity Problems discussed in the literature. The algorithm searches a finite number of nested intervals \([\bar{l}, \bar{u}]\) in such a way that, in each iteration, either an eigenvalue is computed in \([\bar{l}, \bar{u}]\) or a certificate of nonexistence of an eigenvalue in \([\bar{l}, \bar{u}]\) is provided. A hybrid method that combines an enumerative method [1] and a semi-smooth algorithm [2] is discussed for dealing with the Eigenvalue Complementarity Problem over an interval \([\bar{l}, \bar{u}]\). Computational experience is presented to illustrate the efficacy and efficiency of the proposed techniques.
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Acknowledgments
This research is supported in part by the National Science Foundation under Grant Number CMMI - 0969169, and by a Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science. The authors also thank the two referees and the editor for constructive comments that have helped to improve the presentation in this paper.
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Fernandes, L.M., Júdice, J.J., Sherali, H.D. et al. On the computation of all eigenvalues for the eigenvalue complementarity problem. J Glob Optim 59, 307–326 (2014). https://doi.org/10.1007/s10898-014-0165-3
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DOI: https://doi.org/10.1007/s10898-014-0165-3