ENVELOPE THEOREMS FOR STATIC OPTIMIZATION AND CALCULUS OF VARIATIONS

Joël Blot (1, 2) , Hasan Yilmaz (3, 4)

1 UP1 UFR27 - Université Paris 1 Panthéon-Sorbonne - UFR Mathématiques & Informatique
2 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
3 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation
4 UFR Mathématiques UPCité - UFR Mathématiques [Sciences] - Université Paris Cité

We establish differentiability properties of the value function of problems of Static Optimization in an abstract infinite dimensional setting and we apply that to problems of Calculus of Variations. We lighten the assumptions of existing results, notably by using Gâteaux and Hadamard differentials. Moreover we use recently established Multipliers Rules.

Keywords: Envelope theorem; Static optimization; Calculus of Variations. MSC 2020. 90C31; 90C30; 49J50

Domains: Optimization and Control [math.OC]

Joël Blot, Hasan Yilmaz. ENVELOPE THEOREMS FOR STATIC OPTIMIZATION AND CALCULUS OF VARIATIONS. 2021. ⟨hal-03323994⟩