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On the Uniform Nonsingularity Property for Linear Transformations on Euclidean Jordan Algebras

Author

Listed:
  • Roman Sznajder

    (Bowie State University)

  • M. Seetharama Gowda

    (University of Maryland)

  • Jiyuan Tao

    (Loyola University Maryland)

Abstract

In a recent paper, Chua and Yi introduced the so-called uniform nonsingularity property for a nonlinear transformation on a Euclidean Jordan algebra and showed that it implies the global uniqueness property in the context of symmetric cone complementarity problems. In a related paper, Chua, Lin, and Yi raise the question of converse. In this paper, we show that, for linear transformations, the uniform nonsingularity property is inherited by principal subtransformations and, on simple algebras, it is invariant under the action of cone automorphisms. Based on these results, we answer the question of Chua, Lin, and Yi in the negative.

Suggested Citation

  • Roman Sznajder & M. Seetharama Gowda & Jiyuan Tao, 2012. "On the Uniform Nonsingularity Property for Linear Transformations on Euclidean Jordan Algebras," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 306-319, May.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:2:d:10.1007_s10957-011-9964-6
    DOI: 10.1007/s10957-011-9964-6
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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.
    2. 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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