Bornological Coderivative and Subdifferential Calculus in Smooth Banach Spaces

Abstract

In this paper, we study bornological generalized differential properties of sets with nonsmooth boundaries, nonsmooth functions, and set-valued mappings in smooth Banach spaces. We establish a fuzzy intersection rule for bornological normal cones and develop fuzzy calculus for bornological generalized differential constructions as well as exact calculus for the limiting counterparts of these constructions.

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Acknowledgements

We are grateful to anonymous referees for their valuable suggestions and remarks that allowed us to improve the original presentation.

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Correspondence to Nguyen Mau Nam.

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Dedicated to Boris S. Mordukhovich on the occasion of his 70th birthday

Research of Nguyen Mau Nam was partly supported by the National Science Foundation under grant DMS-1716057. Hung M. Phan was partly supported by Autodesk Inc. via a gift made to the Department of Mathematical Sciences, University of Massachusetts Lowell.

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Nam, N.M., Phan, H.M. & Wang, B. Bornological Coderivative and Subdifferential Calculus in Smooth Banach Spaces. Set-Valued Var. Anal 27, 971–993 (2019). https://doi.org/10.1007/s11228-018-0503-6

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Keywords

  • Bornology
  • Generalized differentiation
  • Bornological subdifferential
  • Bornological normal cone
  • Bornological coderivative

Mathematics Subject Classifications (2010)

  • Primary 49J52, 49J53
  • Secondary 90C30