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.
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O. P. Ferreira was supported in part by FUNAPE/UFG, CNPq Grants 201112/2009-4, 475647/2006-8 and PRONEX–Optimization (FAPERJ/CNPq). A. N. Iusem was supported in part by CNPq grant no. 301280/86 and PRONEX-Otimização (FAPERJ/CNPq). S. Z. Németh was supported in part by the Hungarian Research Grant OTKA 60480.
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Ferreira, O.P., Iusem, A.N. & Németh, S.Z. Projections onto convex sets on the sphere. J Glob Optim 57, 663–676 (2013). https://doi.org/10.1007/s10898-012-9914-3
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DOI: https://doi.org/10.1007/s10898-012-9914-3