Nonlinear Transversality Properties of Collections of Sets: Dual Space Necessary Characterizations

Nguyen Duy Cuong (ndcuongctu.edu.vn)
Alexander Y. Kruger (a.krugerfederation.edu.au)

Abstract: This paper continues the study of ‘good arrangements’ of collections of sets in normed vector spaces near a point in their intersection. Our aim is to study general nonlinear transversality properties. We focus on dual space (subdifferential and normal cone) necessary characterizations of these properties. As an application, we provide dual necessary and sufficient conditions for the nonlinear extensions of the new transversality properties of a set-valued mapping to a set in the range space due to Ioffe.

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

Category 1: Convex and Nonsmooth Optimization

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Entry Submitted: 07/02/2019
Entry Accepted: 07/02/2019
Entry Last Modified: 01/30/2020

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