Concepts and techniques of optimization on the sphere
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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.
KeywordsSphere Convex function in the sphere Spheric constrained optimization Variational problem Monotone vector fields
Mathematics Subject Classification26B25 90C25
The authors 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).
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