Nonsmooth sequential analysis in Asplund spaces

Mordukhovich BS & Shao Y (1996). Nonsmooth sequential analysis in Asplund spaces. Transcripts of the American Mathematical Society 348 (4): 1235-1280.

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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 Frechet 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 di erential 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.

Item Type: Article
Research Programs: Dynamic Systems (DYN)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 02:06
Last Modified: 25 Aug 2016 11:43
URI: http://pure.iiasa.ac.at/4684

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