Geodesic
Infimal Convolutions and Lipschitzian Properties of Subdifferentials for Prox-Regular Functions in Hilbert Spaces
Journal of convex analysis, Tome 17 (2010) no. 3, pp. 737-763

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

We study infimal convolutions of extended-real-valued functions in Hilbert spaces paying a special attention to the rather broad and remarkable class of prox-regular functions. Such functions have been well recognized as highly important in many aspects of variational analysis and its applications in both finite-dimensional and infinite-dimensional settings. Based on advanced variational techniques, we discover some new subdifferential properties of infimal convolutions and apply them to the study of Lipschitzian behavior of subdifferentials for prox-regular functions in Hilbert spaces. It is shown, in particular, that the fulfillment of a natural Lipschitz-like property for (set-valued) subdifferentials of prox-regular functions forces such functions, under weak assumptions, actually to be locally smooth with single-valued subdifferentials reduced to Lipschitz continuous gradient mappings.
Classification : 49J52, 46C05
Mots-clés : Subdifferentials, Lipschitz continuity, infimal convolutions, prox-regular functions, prox-bounded functions, set-valued mappings 
@article{JCA_2010_17_3_JCA_2010_17_3_a3,
     author = {M. Bacak and J. M. Borwein and A. Eberhard and B. S. Mordukhovich},
     title = {Infimal {Convolutions} and {Lipschitzian} {Properties} of {Subdifferentials} for {Prox-Regular} {Functions} in {Hilbert} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {737--763},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2010},
     url = {http://geodesic.mathdoc.fr/item/JCA_2010_17_3_JCA_2010_17_3_a3/}
}
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M. Bacak; J. M. Borwein; A. Eberhard; B. S. Mordukhovich. Infimal Convolutions and Lipschitzian Properties of Subdifferentials for Prox-Regular Functions in Hilbert Spaces. Journal of convex analysis, Tome 17 (2010) no. 3, pp. 737-763. http://geodesic.mathdoc.fr/item/JCA_2010_17_3_JCA_2010_17_3_a3/