@article{iiasa4684, volume = {348}, number = {4}, month = {April}, title = {Nonsmooth sequential analysis in Asplund spaces}, year = {1996}, pages = {1235--1280}, journal = {Transcripts of the American Mathematical Society}, url = {http://www.ams.org/journals/tran/1996-348-04/S0002-9947-96-01543-7/S0002-9947-96-01543-7.pdf}, issn = {0002-9947}, 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.}, author = {Mordukhovich, B. S. and Shao, Y.} }