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...
References
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Bersani, A., dell’Isola, F., Seppecher, P. (2020). Lagrange Multipliers in Infinite Dimensional Spaces, Examples of Application. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_266-2
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DOI: https://doi.org/10.1007/978-3-662-53605-6_266-2
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Lagrange Multipliers in Infinite Dimensional Spaces, Examples of Application- Published:
- 25 October 2019
DOI: https://doi.org/10.1007/978-3-662-53605-6_266-2
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Lagrange Multipliers in Infinite Dimensional Spaces, Examples of Application- Published:
- 24 September 2019
DOI: https://doi.org/10.1007/978-3-662-53605-6_266-1