Rotund norms, Clarke subdifferentials and extensions of Lipschitz functions

2002 ◽  
Vol 48 (2) ◽  
pp. 287-301
Author(s):  
Jon Borwein ◽  
John Giles ◽  
Jon Vanderwerff
Keyword(s):  
Lipschitz Functions ◽  
Clarke Subdifferentials

scholarly journals Lipschitz functions with maximal Clarke subdifferentials are staunch

2005 ◽  
Vol 72 (3) ◽  
pp. 491-496 ◽  
Author(s):  
Jonathan M. Borwein ◽  
Xianfu Wang
Keyword(s):  
Banach Space ◽  
Separable Banach Space ◽  
Lipschitz Functions ◽  
Clarke Subdifferential ◽  
Clarke Subdifferentials

In a recent paper we have shown that most non-expansive Lipschitz functions (in the sense of Baire's category) have a maximal Clarke subdifferential. In the present paper, we show that in a separable Banach space the set of non-expansive Lipschitz functions with a maximal Clarke subdifferential is not only generic, but also staunch in the space of non-expansive functions.

On two simple decompositions of Lipschitz functions

Optimization ◽  
2008 ◽  
Vol 57 (2) ◽  
pp. 249-261 ◽  
Author(s):  
S. Zlobec
Keyword(s):  
Lipschitz Functions

scholarly journals Vector variational inequalities and their relations with vector optimization

2013 ◽  
Vol 4 (1) ◽  
pp. 35-44 ◽  
Author(s):  
Surjeet Kaur Suneja ◽  
Bhawna Kohli
Keyword(s):  
Variational Inequalities ◽  
Vector Optimization ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Clarke Subdifferential ◽  
Vector Variational Inequalities ◽  
Regularity Assumption ◽  
Weak Minimum ◽  
Minimum Solution ◽  
Clarke Subdifferentials

In this paper, K- quasiconvex, K- pseudoconvex and other related functions have been introduced in terms of their Clarke subdifferentials, where   is an arbitrary closed convex, pointed cone with nonempty interior. The (strict, weakly) -pseudomonotonicity, (strict) K- naturally quasimonotonicity and K- quasimonotonicity of Clarke subdifferential maps have also been defined. Further, we introduce Minty weak (MVVIP) and Stampacchia weak (SVVIP) vector variational inequalities over arbitrary cones. Under regularity assumption, we have proved that a weak minimum solution of vector optimization problem (VOP) is a solution of (SVVIP) and under the condition of K- pseudoconvexity we have obtained the converse for MVVIP (SVVIP). In the end we study the interrelations between these with the help of strict K-naturally quasimonotonicity of Clarke subdifferential map.

Fourier-Bessel Dini Lipschitz functions in the space $$L_{\alpha ,n}^{2}$$ L α , n 2

2017 ◽  
Vol 28 (7-8) ◽  
pp. 1157-1165 ◽  
Author(s):  
S. El Ouadih ◽  
R. Daher
Keyword(s):  
Lipschitz Functions
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