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On the Solution of the Inverse Eigenvalue Complementarity Problem

Author

Listed:
  • Carmo P. Brás

    (Universidade Nova de Lisboa)

  • Joaquim J. Júdice

    (Instituto de Telecomunicações)

  • Hanif D. Sherali

    (Virginia Tech.)

Abstract

In this paper, we discuss the solution of an Inverse Eigenvalue Complementarity Problem. Two nonlinear formulations are presented for this problem. A necessary and sufficient condition for a stationary point of the first of these formulations to be a solution of the problem is established. On the other hand, to assure global convergence to a solution of this problem when it exists, an enumerative algorithm is designed by exploiting the structure of the second formulation. The use of additional implied constraints for enhancing the efficiency of the algorithm is also discussed. Computational results are provided to highlight the performance of the algorithm.

Suggested Citation

  • Carmo P. Brás & Joaquim J. Júdice & Hanif D. Sherali, 2014. "On the Solution of the Inverse Eigenvalue Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 162(1), pages 88-106, July.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:1:d:10.1007_s10957-013-0464-8
    DOI: 10.1007/s10957-013-0464-8
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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. Pedro Gajardo & Alberto Seeger, 2012. "Reconstructing a matrix from a partial sampling of Pareto eigenvalues," Computational Optimization and Applications, Springer, vol. 51(3), pages 1119-1135, April.
    3. 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.
    4. 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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