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Transactions of the American Mathematical Society

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Nonsmooth sequential analysis in Asplund spaces

Authors: Boris S. Mordukhovich and Yongheng Shao
Journal: Trans. Amer. Math. Soc. 348 (1996), 1235-1280
MSC (1991): Primary 49J52; Secondary 46B20, 58C20
MathSciNet review: 1333396
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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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Additional Information

Boris S. Mordukhovich
Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202

Yongheng Shao
Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202

Keywords: Nonsmooth analysis, generalized differentiation, nonconvex calculus, Asplund spaces, variational principles, Fr\'{e}chet normals and subdifferentials, sequential limits
Received by editor(s): June 8, 1994
Received by editor(s) in revised form: April 3, 1995
Additional Notes: This research was partially supported by the National Science Foundation under grants DMS–9206989 and DMS-9404128
Article copyright: © Copyright 1996 American Mathematical Society

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