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Primal Space Necessary Characterizations of Transversality Properties

Nguyen Duy Cuong (ndcuong***at***ctu.edu.vn)
Alexander Y. Kruger (a.kruger***at***federation.edu.au)

Abstract: This paper continues the study of general nonlinear transversality properties of collections of sets and focuses on primal space necessary (in some cases also sufficient) characterizations of the properties. We formulate geometric, metric and slope characterizations, particularly in the convex setting. The Holder case is given a special attention. Quantitative relations between the nonlinear transversality properties of collections of sets and the corresponding regularity properties of set-valued mappings as well as two nonlinear transversality properties of a convex set-valued mapping to a convex set in the range space are discussed.

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

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Positivity (2021) 25:531558 https://doi.org/10.1007/s11117-020-00775-5

Download: [PDF]

Entry Submitted: 01/22/2020
Entry Accepted: 01/23/2020
Entry Last Modified: 04/17/2021

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