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Geometric and Metric Characterizations of Transversality Properties

Hoa T. Bui (h.bui***at***federation.edu.au)
Nguyen Duy Cuong (ndcuong***at***ctu.edu.vn)
Alexander Y. Kruger (a.kruger***at***federation.edu.au)

Abstract: This paper continues the study of ‘good arrangements’ of collections of sets near a point in their intersection. Our aim is to clarify the relations between various quantitative geometric and metric characterizations of the transversality properties of collections of sets and the corresponding regularity properties of set-valued mappings. We expose all the parameters involved in the definitions and characterizations and establish relationships between them. This allows us to classify all quantitative geometric and metric characterizations of transversality and regularity, and subdivide them into two groups with complete exact equivalences between the parameters within each group and clear relations between the values of the parameters in different groups.

Keywords: Transversality, Subtransversality, Semitransversality, Regularity, Subregularity, Semiregularity

Category 1: Convex and Nonsmooth Optimization

Citation: Vietnam Journal of Mathematics (2020) 48:277–297 https://doi.org/10.1007/s10013-020-00388-1

Download: [PDF]

Entry Submitted: 07/05/2019
Entry Accepted: 07/06/2019
Entry Last Modified: 04/17/2021

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