Extremal cubics on the circle and the 2-sphere

Roland Hildebrand (1) , Anastasia Ivanova (2, 1)

1 DAO - Données, Apprentissage et Optimisation
2 HSE - Vysšaja škola èkonomiki = National Research University Higher School of Economics [Moscow]

We study balls of homogeneous cubics on Rn, n=2,3, which are bounded by unity on the unit sphere. For n=2 we completely describe the facial structure of this norm ball, while for n=3 we classify all extremal points and describe some families of faces.

Mots clés: extremal cubics; homogeneous cubics; norm ball; facial structure

Domaines: Optimisation et contrôle [math.OC]

Roland Hildebrand, Anastasia Ivanova. Extremal cubics on the circle and the 2-sphere. Results in mathematics = Resultate der Mathematik, 2022, 77, pp.135. ⟨10.1007/s00025-022-01659-8⟩. ⟨hal-03385303⟩