Article Dans Une Revue Journal of Convex Analysis Année : 2024

When is a Minkowski norm strictly sub-convex?

Stéphane Simon
Patrick Verovic

Résumé

The aim of this paper is to give two complete and simple characterizations of Minkowski norms N on an arbitrary topological real vector space such that the sublevel sets of N are strictly convex. We first show that this property is equivalent to the continuity of N together with the fact that any open chord between two points of the boundary of the sublevel set N^{-1}([0, 1)) lies inside that set (geometric characterization). On the other hand, we prove that this is also the same as saying that N is continuous and that for an arbitrary real number α > 1 the function N^α is strictly convex (analytic characterization).

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hal-03683717 , version 1 (01-06-2022)

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Stéphane Simon, Patrick Verovic. When is a Minkowski norm strictly sub-convex?. Journal of Convex Analysis, 2024, 31 (1), pp.139-178. ⟨hal-03683717⟩
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