Journal of Convex Analysis 27 (2020), No. 1, 285--306
Copyright Heldermann Verlag 2020
Nonlinear Transversality of Collections of Sets: Dual Space Necessary Characterizations
Nguyen Duy Cuong
Centre for Informatics and Applied Optimization, School of Science, Engineering and Information Technology, Federation University of Australia, Ballarat, Vic. 3350, Australia
duynguyen@students.federation.edu.au
Alexander Y. Kruger
Centre for Informatics and Applied Optimization, School of Science, Engineering and Information Technology, Federation University of Australia, Ballarat, Vic. 3350, Australia
a.kruger@federation.edu.au
This paper continues the study of "good arrangements" of collections of sets in normed 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 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, slope, subdifferential, normal cone.
MSC: 49J52, 49J53; 49K40, 90C30, 90C46.
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