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Linear Complementarity Problems over Symmetric Cones: Characterization of Q b -transformations and Existence Results

Author

Listed:
  • Julio López

    (Universidad Técnica Federico Santa María)

  • Rúben López

    (Universidad Católica de la Santísima Concepción)

  • Héctor C. Ramírez

    (Universidad de Chile)

Abstract

This paper is devoted to the study of the symmetric cone linear complementarity problem (SCLCP). Specifically, our aim is to characterize the class of linear transformations for which the SCLCP has always a nonempty and bounded solution set in terms of larger classes. For this, we introduce a couple of new classes of linear transformations in this SCLCP context. Then, we study them for concrete particular instances (such as second-order and semidefinite linear complementarity problems) and for specific examples (Lyapunov, Stein functions, among others). This naturally permits to establish coercive and noncoercive existence results for SCLCPs.

Suggested Citation

  • Julio López & Rúben López & Héctor C. Ramírez, 2013. "Linear Complementarity Problems over Symmetric Cones: Characterization of Q b -transformations and Existence Results," Journal of Optimization Theory and Applications, Springer, vol. 159(3), pages 741-768, December.
    • Handle: RePEc:spr:joptap:v:159:y:2013:i:3:d:10.1007_s10957-012-0116-4
    DOI: 10.1007/s10957-012-0116-4
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    References listed on IDEAS

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    1. M. Seetharama Gowda & Roman Sznajder, 2006. "Automorphism Invariance of P - and GUS -Properties of Linear Transformations on Euclidean Jordan Algebras," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 109-123, February.
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