Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Lagrange Multipliers in Infinite Dimensional Spaces, Examples of Application

  • A. Bersani
  • F. dell’IsolaEmail author
  • P. Seppecher
Living reference work entry

Latest version View entry history

DOI: https://doi.org/10.1007/978-3-662-53605-6_266-2

Synonyms

Definitions

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 the 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.

Introduction

In this entry we show that the theorem of Lagrange multipliers in infinite-dimensional systems (dell’Isola and Di Cosmo, 2018) can be a very powerful tool for dealing with constrained problems also in infinite-dimensional spaces. This tool is powerful but must be used...

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringSapienza UniversityRomeItaly
  2. 2.Dipartimento di Ingegneria Strutturale e GeotecnicaUniversità degli Studi di Roma “La Sapienza”RomeItaly
  3. 3.Dipartimento di Ingegneria Civile, Edile-Architettura e AmbientaleUniversità degli Studi dell’AquilaL’AquilaItaly
  4. 4.International Research Center for the Mathematics and Mechanics of Complex SystemsL’AquilaItaly
  5. 5.Institut de MathématiquesUniversité de ToulonToulonFrance

Section editors and affiliations

  • F. dell’Isola
    • 1
    • 2
    • 3
  1. 1.Dipartimento di Ingegneria Strutturale e GeotecnicaUniversità degli Studi di Roma “La Sapienza”RomeItaly
  2. 2.Dipartimento di Ingegneria Civile, Edile-Architettura e AmbientaleUniversità degli Studi dell’AquilaL’AquilaItaly
  3. 3.International Research Center for the Mathematics and Mechanics of Complex SystemsL’AquilaItaly