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Convexity of Non-homogeneous Quadratic Functions on the Hyperbolic Space

Author

Listed:
  • Orizon P. Ferreira

    (Universidade Federal de Goiás)

  • Sándor Z. Németh

    (University of Birmingham)

  • Jinzhen Zhu

    (University of Birmingham)

Abstract

In this paper, some concepts related to the intrinsic convexity of non-homogeneous quadratic functions on the hyperbolic space are studied. Unlike in the Euclidean space, the study of intrinsic convexity of non-homogeneous quadratic functions in the hyperbolic space is more elaborate than that of homogeneous quadratic functions. Several characterizations that allow the construction of many examples will be presented.

Suggested Citation

  • Orizon P. Ferreira & Sándor Z. Németh & Jinzhen Zhu, 2023. "Convexity of Non-homogeneous Quadratic Functions on the Hyperbolic Space," Journal of Optimization Theory and Applications, Springer, vol. 199(3), pages 1085-1105, December.
    • Handle: RePEc:spr:joptap:v:199:y:2023:i:3:d:10.1007_s10957-023-02332-y
    DOI: 10.1007/s10957-023-02332-y
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    References listed on IDEAS

    as
    1. O. P. Ferreira & S. Z. Németh, 2019. "On the spherical convexity of quadratic functions," Journal of Global Optimization, Springer, vol. 73(3), pages 537-545, March.
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    Cited by:

    1. Ryan Bolton & Sándor Zoltán Németh, 2025. "Why Study Spherical Convexity of Non-Homogeneous Quadratics and what Makes it Surprising?," Journal of Optimization Theory and Applications, Springer, vol. 205(1), pages 1-26, April.

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