- Title
- Infimal convolutions and lipschitzian properties of subdifferentials for prox-regular functions in hilbert spaces
- Creator
- Bačák, Miroslav; Borwein, Jonathan M.; Eberhard, Andrew; Mordukhovich, Boris S.
- Relation
- Journal of Convex Analysis Vol. 17, Issue 3-4, p. 737-763
- Relation
- http://www.heldermann.de/JCA/JCA17/jca17.htm#jca173
- Publisher
- Heldermann Verlag
- Resource Type
- journal article
- Date
- 2010
- Description
- 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.
- Subject
- subdifferentials; Lipschitz continuity; infimal convolutions; prox-regular functions; prox-bounded functions; set-valued mappings
- Identifier
- http://hdl.handle.net/1959.13/926680
- Identifier
- uon:9909
- Identifier
- ISSN:0944-6532
- Language
- eng
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