Rank theorem in infinite dimension and lagrange multipliers

Joël Blot (1, 2)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
2 UP1 - Université Paris 1 Panthéon-Sorbonne

We use an extension to the infinite dimension of the rank theorem of the differential calculus to establish a Karush-Huhn-Tucker theorem for optimization problems in Banach spaces. We provide an application to variational problems on bounded processus under equality constraints.

Mots clés: Rank theorem; Lagrange multipliers; Banach spaces Classification MSC 2010: 49K27; 49K30

Domaines: Optimisation et contrôle [math.OC]

Joël Blot. Rank theorem in infinite dimension and lagrange multipliers. 2018. ⟨hal-01611305v2⟩