Lagrange multipliers in infinite dimensional spaces, examples of application

A. Bersani (1) , F. Dell'Isola (2, 3) , Pierre Seppecher (4)

1 SBAI - Dipartimento di Scienze di Base e Applicate per l'Ingegneria
2 MEMOCS - International Research Center for the Mathematics & Mechanics of Complex Systems
3 DISG - Dipartimento di Ingegneria Strutturale e Geotecnica
4 IMATH - Institut de Mathématiques de Toulon - EA 2134

The Lagrange multipliers method is used in Mathematical Analysis, in Mechanics, in Economics and in several other fields, to deal with the search of the global maximum or minimum of a function, in presence of a constraint. The usual technique, applied to the case of finite-dimensional systems, transforms the constrained optimization problem into an unconstrained one, by means of the introduction of one or more multipliers and of a suitable Lagrangian function, to be optimized. In Mechanics, several optimization problems can be applied to infinite-dimensional systems. Lagrange multipliers method can be applied also to these cases.

Mots clés: Infinite-dimensional constrained mechanical systems

Domaines: Physique mathématique [math-ph]; Mécanique [physics]

A. Bersani, F. Dell'Isola, Pierre Seppecher. Lagrange multipliers in infinite dimensional spaces, examples of application. 2019. ⟨hal-02269765⟩