Some New Characterizations of Intrinsic Transversality in Hilbert Spaces

Journal article (2020)

Authors

Hieu Thao Nguyen Team Raf Van de Plas - Mechanical, Maritime and Materials Engineering , Can Tho University
Hoa T. Bui Curtin University
Duy Cuong Nguyen Can Tho University, Federation University Australia
M.H.G. Verhaegen Team Raf Van de Plas - Mechanical, Maritime and Materials Engineering
Research Group
Team Raf Van de Plas (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2020 Hieu Thao Nguyen, Hoa T. Bui, Duy Cuong Nguyen, M.H.G. Verhaegen
DOI: https://doi.org/10.1007/s11228-020-00531-7
Transversality Subtransversality Intrinsic transversality Normal cone Relative normal cone
More Info
expand_more

Published Date

2020

Language

English

Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Raf Van de Plas

Abstract

Motivated by a number of questions concerning transversality-type properties of pairs of sets recently raised by Ioffe and Kruger, this paper reports several new characterizations of the intrinsic transversality property in Hilbert spaces. New results in terms of normal vectors clarify the picture of intrinsic transversality, its variants and sufficient conditions for subtransversality, and unify several of them. For the first time, intrinsic transversality is characterized by an equivalent condition which does not involve normal vectors. This characterization offers another perspective on intrinsic transversality. As a consequence, the obtained results allow us to answer a number of important questions about transversality-type properties.