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Some characterizations of cone preserving Z-transformations

Author

Listed:
  • M. Seetharama Gowda

    (University of Maryland, Baltimore County)

  • Yoon J. Song

    (Soongsil University)

  • K. C. Sivakumar

    (Indian Institute of Technology Madras)

Abstract

Given a proper cone K in a finite dimensional real Hilbert space H, we present some results characterizing $$\mathbf{Z}$$Z-transformations that keep K invariant. We show for example, that when K is irreducible, nonnegative multiples of the identity transformation are the only such transformations. And when K is reducible, they become ‘nonnegative diagonal’ transformations. We apply these results to symmetric cones in Euclidean Jordan algebras, and, in particular, obtain conditions on the Lyapunov transformation $$L_A$$LA and the Stein transformation $$S_A$$SA that keep the semidefinite cone invariant.

Suggested Citation

  • M. Seetharama Gowda & Yoon J. Song & K. C. Sivakumar, 2020. "Some characterizations of cone preserving Z-transformations," Annals of Operations Research, Springer, vol. 287(2), pages 727-736, April.
    • Handle: RePEc:spr:annopr:v:287:y:2020:i:2:d:10.1007_s10479-017-2439-x
    DOI: 10.1007/s10479-017-2439-x
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    References listed on IDEAS

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    1. 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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