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More results on column sufficiency property in Euclidean Jordan algebras

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Abstract

A matrix M∈R n×n is said to be a column sufficient matrix if the solution set of LCP(M,q) is convex for every q∈R n. In a recent article, Qin et al. (Optim. Lett. 3:265–276, 2009) studied the concept of column sufficiency property in Euclidean Jordan algebras. In this paper, we make a further study of this concept and prove numerous results relating column sufficiency with the Z and Lypaunov-like properties. We also study this property for some special linear transformations.

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Acknowledgements

We would like to thank three anonymous referees for their very constructive suggestions and comments. We thank Dr. K.C. Sivakumar, IIT Madras, India, for his comments and suggestions. The first author would like to thank Dr. K.C. Sivakumar for inviting him to IIT Madras, where part of the work was carried out. Also, the first author would like to thank the dean of Loyola College for travel support.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Loyola University Maryland, Baltimore, MD, 21210, USA

    J. Tao

  2. The Institute of Mathematical Sciences, Chennai, 600113, India

    I. Jeyaraman

  3. Indian Statistical Institute, Chennai, India

    G. Ravindran

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  1. J. Tao
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  2. I. Jeyaraman
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  3. G. Ravindran
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Correspondence to J. Tao.

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Tao, J., Jeyaraman, I. & Ravindran, G. More results on column sufficiency property in Euclidean Jordan algebras. Ann Oper Res 243, 229–243 (2016). https://doi.org/10.1007/s10479-013-1459-4

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  • DOI: https://doi.org/10.1007/s10479-013-1459-4

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