Projections onto convex sets on the sphere
Journal of Global Optimization, 2013•Springer
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.
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.
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.
Springer
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