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On the Spherical Quasi-convexity of Quadratic Functions on Spherically Subdual Convex Sets

Author

Listed:
  • Orizon Pereira Ferreira

    (Universidade Federal de Goiás)

  • Sándor Zoltán Németh

    (University of Birmingham)

  • Lianghai Xiao

    (University of Birmingham)

Abstract

In this paper, the spherical quasi-convexity of quadratic functions on spherically subdual convex sets is studied. Sufficient conditions for spherical quasi-convexity on spherically subdual convex sets are presented. A partial characterization of spherical quasi-convexity on spherical Lorentz sets is given, and some examples are provided.

Suggested Citation

  • Orizon Pereira Ferreira & Sándor Zoltán Németh & Lianghai Xiao, 2020. "On the Spherical Quasi-convexity of Quadratic Functions on Spherically Subdual Convex Sets," Journal of Optimization Theory and Applications, Springer, vol. 187(1), pages 1-21, October.
    • Handle: RePEc:spr:joptap:v:187:y:2020:i:1:d:10.1007_s10957-020-01741-7
    DOI: 10.1007/s10957-020-01741-7
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    References listed on IDEAS

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    1. O. Ferreira & A. Iusem & S. Németh, 2013. "Projections onto convex sets on the sphere," Journal of Global Optimization, Springer, vol. 57(3), pages 663-676, November.
    2. 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.
    3. O. Ferreira & A. Iusem & S. Németh, 2014. "Concepts and techniques of optimization on the sphere," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 1148-1170, October.
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    Cited by:

    1. Erik Alex Papa Quiroz, 2024. "Proximal Point Method for Quasiconvex Functions in Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1268-1285, September.

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