Concepts and techniques of optimization on the sphere

O. P. Ferreira ^[2] ; A. N. Iusem ^[3] ; S. Z. Németh ^[1]
1. [1] University of Birmingham
  
  University of Birmingham
  
  Reino Unido
2. [2] IME/UFG, Brasil
3. [3] Instituto de Matemática Pura e Aplicada, Brasil
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Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 22, Nº. 3, 2014, págs. 1148-1170
Idioma: inglés
DOI: 10.1007/s11750-014-0322-3
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Resumen
- 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.