Abstract
Th e geo desic convexity of the positive orthant and different functions related mainly to potential functions are studied with respect to the affine and other Riemann ian metrics. For the affine metric. the geodesic co nvexi ty of geometric optimization problems and the fulfilment of the Hopf-Rinow theorem are shown. Finally, the geodesic convexity property of separable functions with respect to Riemannian metrics generated by other separable functions is investigated.
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