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On the spherical convexity of quadratic functions

Author

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  • O. P. Ferreira

    (IME/UFG, Avenida Esperança, s/n, Campus Samambaia)

  • S. Z. Németh

    (University of Birmingham)

Abstract

In this paper we study the spherical convexity of quadratic functions on spherically convex sets. In particular, conditions characterizing the spherical convexity of quadratic functions on spherical convex sets associated to the positive orthants and Lorentz cone are given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:73:y:2019:i:3:d:10.1007_s10898-018-0710-6
    DOI: 10.1007/s10898-018-0710-6
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    References listed on IDEAS

    as
    1. 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.
    2. Zvi Drezner & George O. Wesolowsky, 1983. "Minimax and maximin facility location problems on a sphere," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 30(2), pages 305-312, June.
    3. Laurent, M., 2009. "Sums of squares, moment matrices and optimization over polynomials," Other publications TiSEM 9fef820b-69d2-43f2-a501-e, Tilburg University, School of Economics and Management.
    4. 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.
    5. Sándor Zoltán Németh & George Isac, 2008. "Scalar and Asymptotic Scalar Derivatives," Springer Optimization and Its Applications, Springer, number 978-0-387-73988-5, June.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. 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.
    2. Dezhou Kong & Lishan Liu & Yonghong Wu, 2020. "Isotonicity of Proximity Operators in General Quasi-Lattices and Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 187(1), pages 88-104, October.
    3. Van-Bong Nguyen & Thi Ngan Nguyen & Ruey-Lin Sheu, 2020. "Strong duality in minimizing a quadratic form subject to two homogeneous quadratic inequalities over the unit sphere," Journal of Global Optimization, Springer, vol. 76(1), pages 121-135, January.

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