# Differentials and Semidifferentials for Metric Spaces of Shapes and Geometries

Abstract : The Hadamard semidifferential retains the advantages of the differential calculus such as the chain rule and semiconvex functions are Hadamard semidifferentiable. The semidifferential calculus extends to subsets of ${\mathbb {R}}^n$ without Euclidean smooth structure. This set-up is an ideal tool to study the semidifferentiability of objective functions with respect to families of sets which are non-linear non-convex complete metric spaces. Shape derivatives are differentials for spaces endowed with Courant metrics. Topological derivatives are shown to be semidifferentials on the group of Lebesgue measurable characteristic functions.
Keywords :
Type de document :
Communication dans un congrès
Lorena Bociu; Jean-Antoine Désidéri; Abderrahmane Habbal. 27th IFIP Conference on System Modeling and Optimization (CSMO), Jun 2015, Sophia Antipolis, France. Springer International Publishing, IFIP Advances in Information and Communication Technology, AICT-494, pp.230-239, 2016, System Modeling and Optimization. 〈10.1007/978-3-319-55795-3_21〉
Domaine :

Littérature citée [14 références]

https://hal.inria.fr/hal-01626899
Contributeur : Hal Ifip <>
Soumis le : mardi 31 octobre 2017 - 14:40:43
Dernière modification le : mardi 31 octobre 2017 - 14:44:59
Document(s) archivé(s) le : jeudi 1 février 2018 - 13:59:00

### Fichier

##### Accès restreint
Fichier visible le : 2019-01-01

Connectez-vous pour demander l'accès au fichier

### Citation

Michel Delfour. Differentials and Semidifferentials for Metric Spaces of Shapes and Geometries. Lorena Bociu; Jean-Antoine Désidéri; Abderrahmane Habbal. 27th IFIP Conference on System Modeling and Optimization (CSMO), Jun 2015, Sophia Antipolis, France. Springer International Publishing, IFIP Advances in Information and Communication Technology, AICT-494, pp.230-239, 2016, System Modeling and Optimization. 〈10.1007/978-3-319-55795-3_21〉. 〈hal-01626899〉

### Métriques

Consultations de la notice