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A New Method for Solving Second-Order Cone Eigenvalue Complementarity Problems

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Abstract

In this paper, we study numerical methods for solving eigenvalue complementarity problems involving the product of second-order cones (or Lorentz cones). We reformulate such problem to find the roots of a semismooth function. An extension of the Lattice Projection Method (LPM) to solve the second-order cone eigenvalue complementarity problem is proposed. The LPM is compared to the semismooth Newton methods, associated to the Fischer–Burmeister and the natural residual functions. The performance profiles highlight the efficiency of the LPM. A globalization of these methods, based on the smoothing and regularization approaches, are discussed.

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Notes

  1. As stopping criteria, we use \(\Vert \varPhi (z^k)\Vert < 10^{-8}\).

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Acknowledgments

We thank the three anonymous reviewers for their constructive comments, which helped us to improve the initial version of our manuscript.

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Authors and Affiliations

  1. XLIM UMR-CNRS 7252, Université de Limoges, 870 60, Limoges, France

    Samir Adly & Hadia Rammal

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  1. Samir Adly
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  2. Hadia Rammal
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Correspondence to Samir Adly.

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Communicated by Asen L. Dontchev.

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Adly, S., Rammal, H. A New Method for Solving Second-Order Cone Eigenvalue Complementarity Problems. J Optim Theory Appl 165, 563–585 (2015). https://doi.org/10.1007/s10957-014-0645-0

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