Nonsmooth sequential analysis in Asplund spaces |
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Authors: | Boris S Mordukhovich Yongheng Shao |
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Institution: | Department of Mathematics, Wayne State University, Detroit, Michigan 48202 ; Department of Mathematics, Wayne State University, Detroit, Michigan 48202 |
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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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Keywords: | Nonsmooth analysis generalized differentiation nonconvex calculus Asplund spaces variational principles Fr\'{e}chet normals and subdifferentials sequential limits |
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