Nonsmooth sequential analysis in Asplund spaces

Mordukhovich, Boris; Shao, Yongheng

doi:10.1090/S0002-9947-96-01543-7

Nonsmooth sequential analysis in Asplund spaces
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by Boris S. Mordukhovich and Yongheng Shao

Trans. Amer. Math. Soc. 348 (1996), 1235-1280

DOI: https://doi.org/10.1090/S0002-9947-96-01543-7

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Abstract:

We develop a generalized differentiation theory for nonsmooth functions and sets with nonsmooth boundaries defined in Asplund spaces. This broad subclass of Banach spaces provides a convenient framework for many important applications to optimization, sensitivity, variational inequalities, etc. Our basic normal and subdifferential constructions are related to sequential weak-star limits of Fréchet normals and subdifferentials. Using a variational approach, we establish a rich calculus for these nonconvex limiting objects which turn out to be minimal among other set-valued differential constructions with natural properties. The results obtained provide new developments in infinite dimensional nonsmooth analysis and have useful applications to optimization and the geometry of Banach spaces.

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