Geodesic
Lipschitz-like Property of Subdifferential Mapping of Convex Continuous Functions on Hilbert Space
Journal of convex analysis, Tome 27 (2020) no. 2, pp. 753-776
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A Lipschitz-like property of subdifferential mappings of convex continuous functions on Hilbert spaces is investigated. It is shown that the subdifferential mapping of such a function admits a Lipschitz-like property at all points from a dense subset of its domain. In particular, Lipschitz-like properties of subdifferentials of distance functions from sets with convex complements are discovered.
Classification : 52A41, 49J50
Mots-clés : Convex functions, Aubin Lipschitz-like properties, best approximation, metric projection mapping, Borel sets 
@article{JCA_2020_27_2_JCA_2020_27_2_a16,
     author = {D. Zagrodny},
     title = {Lipschitz-like {Property} of {Subdifferential} {Mapping} of {Convex} {Continuous} {Functions} on {Hilbert} {Space}},
     journal = {Journal of convex analysis},
     pages = {753--776},
     year = {2020},
     volume = {27},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2020_27_2_JCA_2020_27_2_a16/}
}
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D. Zagrodny. Lipschitz-like Property of Subdifferential Mapping of Convex Continuous Functions on Hilbert Space. Journal of convex analysis, Tome 27 (2020) no. 2, pp. 753-776. http://geodesic.mathdoc.fr/item/JCA_2020_27_2_JCA_2020_27_2_a16/