Metric regularity and subdifferential calculus in Banach spaces

1995 ◽  
Vol 3 (1) ◽  
pp. 87-100 ◽  
Author(s):  
A. Jourani ◽  
L. Thibault
Keyword(s):  
Banach Spaces ◽  
Metric Regularity ◽  
Subdifferential Calculus

A general metric regularity in asplund banach spaces

1998 ◽  
Vol 19 (3-4) ◽  
pp. 215-226 ◽  
Author(s):  
T. Amahroq ◽  
A. Jourani ◽  
L. Thibault
Keyword(s):  
Banach Spaces ◽  
Metric Regularity

Extensions Of Subdifferential Calculus Rules in Banach Spaces

1996 ◽  
Vol 48 (4) ◽  
pp. 834-848 ◽  
Author(s):  
A. Jourani ◽  
L. Thibault
Keyword(s):  
Banach Spaces ◽  
Clarke Subdifferential ◽  
Subdifferential Calculus ◽  
Finite Dimensional ◽  
Calculus Rules ◽  
Approximate Subdifferential ◽  
The Clarke Subdifferential

AbstractThis paper is devoted to extending formulas for the geometric approximate subdifferential and the Clarke subdifferential of extended-real-valued functions on Banach spaces. The results are strong enough to include completely the finite dimensional setting.

scholarly journals METRIC REGULARITY OF COMPOSITE MULTIFUNCTIONS IN BANACH SPACES

2009 ◽  
Vol 13 (6A) ◽  
pp. 1723-1735 ◽  
Author(s):  
Xi Yin Zheng ◽  
Kung Fu Ng
Keyword(s):  
Banach Spaces ◽  
Metric Regularity

scholarly journals Restrictive metric regularity and generalized differential calculus in Banach spaces

2004 ◽  
Vol 2004 (50) ◽  
pp. 2653-2680 ◽  
Author(s):  
Boris S. Mordukhovich ◽  
Bingwu Wang
Keyword(s):  
Banach Spaces ◽  
Differential Calculus ◽  
Metric Regularity ◽  
Sufficient Conditions ◽  
Normal Cones ◽  
First Order ◽  
Nonconvex Sets ◽  
Generalized Differential ◽  
Necessary And Sufficient ◽  
Generalized Differential Calculus

We consider nonlinear mappingsf:X→Ybetween Banach spaces and study the notion ofrestrictive metric regularityoffaround some pointx¯, that is, metric regularity offfromXinto the metric spaceE=f(X). Some sufficient as well as necessary and sufficient conditions for restrictive metric regularity are obtained, which particularly include an extension of the classical Lyusternik-Graves theorem in the case whenfis strictly differentiable atx¯but its strict derivative∇f(x¯)is not surjective. We develop applications of the results obtained and some other techniques in variational analysis to generalized differential calculus involving normal cones to nonsmooth and nonconvex sets, coderivatives of set-valued mappings, as well as first-order and second-order subdifferentials of extended real-valued functions.

Bornological Coderivative and Subdifferential Calculus in Smooth Banach Spaces

2019 ◽  
Vol 27 (4) ◽  
pp. 971-993
Author(s):  
Nguyen Mau Nam ◽  
Hung M. Phan ◽  
Bingwu Wang
Keyword(s):  
Banach Spaces ◽  
Subdifferential Calculus
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