Concepts and techniques of optimization on the sphere
In this paper some concepts and techniques of Mathematical Programming are extended in
an intrinsic way from the Euclidean space to the sphere. In particular, the notion of convex
functions, variational problem and monotone vector fields are extended to the sphere and
several characterizations of these notions are shown. As an application of the convexity
concept, necessary and sufficient optimality conditions for constrained convex optimization
problems on the sphere are derived.
an intrinsic way from the Euclidean space to the sphere. In particular, the notion of convex
functions, variational problem and monotone vector fields are extended to the sphere and
several characterizations of these notions are shown. As an application of the convexity
concept, necessary and sufficient optimality conditions for constrained convex optimization
problems on the sphere are derived.
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