Geodesic
Infinite Dimensional Clarke Generalized Jacobian
Journal of convex analysis, Tome 14 (2007) no. 2, pp. 433-454

Voir la notice de l'article provenant de la source Heldermann Verlag

We extend for a locally Lipschitz function the notion of Clarke's generalized Jacobian to the setting where the domain lies in an infinite dimensional normed space. When the function is real-valued this notion reduces to the Clarke's generalized gradient. Using this extension, we obtain an exact smooth-nonsmooth chain rule from which the sum rule and the product rule follow. Also an exact formula for the generalized Jacobian of piecewise differentiable functions will be provided.
Classification : 49A52, 58C20
Mots-clés : Generalized Jacobian, chain rule, sum rule, piecewise smooth functions 
@article{JCA_2007_14_2_JCA_2007_14_2_a12,
     author = {Z. P\'ales and V. Zeidan},
     title = {Infinite {Dimensional} {Clarke} {Generalized} {Jacobian}},
     journal = {Journal of convex analysis},
     pages = {433--454},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2007},
     url = {http://geodesic.mathdoc.fr/item/JCA_2007_14_2_JCA_2007_14_2_a12/}
}
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Z. Páles; V. Zeidan. Infinite Dimensional Clarke Generalized Jacobian. Journal of convex analysis, Tome 14 (2007) no. 2, pp. 433-454. http://geodesic.mathdoc.fr/item/JCA_2007_14_2_JCA_2007_14_2_a12/