Envelope theorems for static optimization and calculus of variations

TL;DR

This paper investigates the differentiability of the value function in static optimization and calculus of variations, using advanced differential concepts and relaxed assumptions to extend existing theoretical results.

Contribution

It introduces new differentiability results for the value function in infinite-dimensional static optimization and calculus of variations, utilizing Gâteaux and Hadamard differentials and recent multiplier rules.

Findings

Established differentiability properties under weaker assumptions

Applied results to calculus of variations problems

Utilized Gâteaux and Hadamard differentials for analysis

Abstract

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 G{\^a}teaux and Hadamard differentials. Moreover we use recently established Multipliers Rules.