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Bases, outils et principes pour l'analyse variationnelle pp 25–58Cite as

CONDITIONS NÉCESSAIRES D’OPTIMALITÉ APPROCHÉE

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Part of the book series: Mathématiques et Applications ((MATHAPPLIC,volume 70))

Abstract

Une condition nécessaire d’optimalité standard affirme que si \(f:E\rightarrow {\mathbb R }\cup \left\{ +\infty \right\} \) est minimisée en \(\overline{x}\) et que \(f\) est différentiable en \(\overline{x}\) (de différentielle \(Df(\overline{x})\)), alors \(Df(\overline{x})=0\). La situation que l’on va examiner dans ce chapitre est celle où il n’y a pas (nécessairement) de minimiseurs de \(f\) sur \(E\) mais seulement des minimiseurs approchés, disons à \(\varepsilon \) près,à

"Good modern science implies good variational problems." M. S. Berger (1983)

"Nous devons nous contenter d’améliorer indéfiniment nos approximations" K. Popper (1984)

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Authors and Affiliations

  1. Institut de Mathématiques de Toulouse, Université Paul Sabatier, route de Narbonne 118, 31062, Toulouse Cedex 9, France

    Jean-Baptiste Hiriart-Urruty

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  1. Jean-Baptiste Hiriart-Urruty
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Correspondence to Jean-Baptiste Hiriart-Urruty .

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Hiriart-Urruty, JB. (2013). CONDITIONS NÉCESSAIRES D’OPTIMALITÉ APPROCHÉE. In: Bases, outils et principes pour l'analyse variationnelle. Mathématiques et Applications, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30735-5_2

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