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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We are grateful to anonymous referees for their valuable suggestions and remarks that allowed us to improve the original presentation.
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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
- Generalized differentiation
- Bornological subdifferential
- Bornological normal cone
- Bornological coderivative
Mathematics Subject Classifications (2010)
- Primary 49J52, 49J53
- Secondary 90C30