Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Transversality
  • subtransversality
  • semitransversality
  • slope
  • subdifferential
  • normal cone

Mathematics Subject Classification

49J52, 49J53; 49K40, 90C30, 90C46

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Suggested citation

N. D. Cuong, A. Y. Kruger. “Nonlinear Transversality of Collections of Sets: Dual Space Necessary Characterizations.” Journal of Convex Analysis 27 (2020), No. 1, 285–306. https://doi.org/10.68381/jca27016

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