Calculus Rules for V -Proximal Subdifferentials in Smooth Banach Spaces
Author
Source
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-06-13
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
In 2010, Bounkhel et al.
introduced new proximal concepts (analytic proximal subdifferential, geometric proximal subdifferential, and proximal normal cone) in reflexive smooth Banach spaces.
They proved, in p -uniformly convex and q -uniformly smooth Banach spaces, the density theorem for the new concepts of proximal subdifferential and various important properties for both proximal subdifferential concepts and the proximal normal cone concept.
In this paper, we establish calculus rules (fuzzy sum rule and chain rule) for both proximal subdifferentials and we prove the Bishop-Phelps theorem for the proximal normal cone.
The limiting concept for both proximal subdifferentials and for the proximal normal cone is defined and studied.
We prove that both limiting constructions coincide with the Mordukhovich constructions under some assumptions on the space.
Applications to nonconvex minimisation problems and nonconvex variational inequalities are established.
American Psychological Association (APA)
Bounkhel, Messaoud. 2016. Calculus Rules for V -Proximal Subdifferentials in Smooth Banach Spaces. Journal of Function Spaces،Vol. 2016, no. 2016, pp.1-12.
https://search.emarefa.net/detail/BIM-1108572
Modern Language Association (MLA)
Bounkhel, Messaoud. Calculus Rules for V -Proximal Subdifferentials in Smooth Banach Spaces. Journal of Function Spaces No. 2016 (2016), pp.1-12.
https://search.emarefa.net/detail/BIM-1108572
American Medical Association (AMA)
Bounkhel, Messaoud. Calculus Rules for V -Proximal Subdifferentials in Smooth Banach Spaces. Journal of Function Spaces. 2016. Vol. 2016, no. 2016, pp.1-12.
https://search.emarefa.net/detail/BIM-1108572
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1108572