6533b836fe1ef96bd12a0829

RESEARCH PRODUCT

Weak regularity of functions and sets in Asplund spaces

Abderrahim Jourani

subject

Discrete mathematicsDimension (vector space)Applied MathematicsPartition regularityMathematics::Optimization and ControlSubderivativeAnalysisMathematics

description

Abstract In this paper, we study a new concept of weak regularity of functions and sets in Asplund spaces. We show that this notion includes prox-regular functions, functions whose subdifferential is weakly submonotone and amenable functions in infinite dimension. We establish also that weak regularity is equivalent to Mordukhovich regularity in finite dimension. Finally, we give characterizations of the weak regularity of epi-Lipschitzian sets in terms of their local representations.

yearjournalcountryeditionlanguage
2006-08-01Nonlinear Analysis: Theory, Methods & Applications
https://doi.org/10.1016/j.na.2005.09.031