Nonsmooth sequential analysis in Asplund spaces
Open Access
- 1 April 1996
- journal article
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 348 (4), 1235-1280
- https://doi.org/10.1090/s0002-9947-96-01543-7
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.Keywords
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