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Strict Semimonotonicity Property of Linear Transformations on Euclidean Jordan Algebras

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  • J. Tao

    (Loyola University Maryland)

Abstract

Motivated by the equivalence of the strict semimonotonicity property of the matrix A and the uniqueness of the solution to the linear complementarity problem LCP(A,q) for q∈R + n , we study the strict semimonotonicity (SSM) property of linear transformations on Euclidean Jordan algebras. Specifically, we show that, under the copositive condition, the SSM property is equivalent to the uniqueness of the solution to LCP(L,q) for all q in the symmetric cone K. We give a characterization of the uniqueness of the solution to LCP(L,q) for a Z transformation on the Lorentz cone ℒ + n . We study also a matrix-induced transformation on the Lorentz space ℒ n .

Suggested Citation

  • J. Tao, 2010. "Strict Semimonotonicity Property of Linear Transformations on Euclidean Jordan Algebras," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 575-596, March.
    • Handle: RePEc:spr:joptap:v:144:y:2010:i:3:d:10.1007_s10957-009-9611-7
    DOI: 10.1007/s10957-009-9611-7
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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. J. Tao, 2009. "Positive Principal Minor Property of Linear Transformations on Euclidean Jordan Algebras," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 131-152, January.
    3. 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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    Cited by:

    1. J. Tao & I. Jeyaraman & G. Ravindran, 2016. "More results on column sufficiency property in Euclidean Jordan algebras," Annals of Operations Research, Springer, vol. 243(1), pages 229-243, August.

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    More about this item

    Keywords

    Euclidean Jordan algebra; P property; SSM property; Copositiveness; Complementarity problem; R0 property; Q property; Z property; GUS property;
    All these keywords.

    JEL classification:

    • R0 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General

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