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Projections onto convex sets on the sphere

Author

Listed:
  • O. Ferreira
  • A. Iusem
  • S. Németh

Abstract

In this paper some concepts of convex analysis are extended in an intrinsic way from the Euclidean space to the sphere. In particular, relations between convex sets in the sphere and pointed convex cones are presented. Several characterizations of the usual projection onto a Euclidean convex set are extended to the sphere and an extension of Moreau’s theorem for projection onto a pointed convex cone is exhibited. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jglopt:v:57:y:2013:i:3:p:663-676
    DOI: 10.1007/s10898-012-9914-3
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    Cited by:

    1. Fabiana R. de Oliveira & Orizon P. Ferreira, 2020. "Newton Method for Finding a Singularity of a Special Class of Locally Lipschitz Continuous Vector Fields on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 522-539, May.
    2. 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.
    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.
    4. 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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