Proceedings of the American Mathematical Society

Author(s): Boris S. Mordukhovich; Bingwu Wang
Journal: Proc. Amer. Math. Soc. 131 (2003), 389-399.
MSC (2000): Primary 49J52; Secondary 58C20
Posted: September 25, 2002
Retrieve article in: PDF DVI PostScript

Abstract: We introduce new differentiability properties of functions between Banach spaces and establish their relationships with graphical regularity of Lipschitzian single-valued and set-valued mappings. The proofs are based on advanced tools of nonsmooth variational analysis including new results on coderivative scalarization and normal cone calculus.

1.: F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York, 1983. MR 85m:49002
2.: N. Dunford and J. T. Schwartz, Linear Operators, Part I, Interscience, New York, 1958. MR 22:8302
3.: M. Fabian, Subdifferentiability and trustworthiness in the light of a new variational principle of Borwein and Preiss, Acta Univ. Carolinae 30 (1989), 51-56. MR 91c:49024
4.: A. D. Ioffe, On subdifferentiability spaces, Ann. New York Acad. Sci. 410 (1983), 107-119. MR 86g:90124
5.: -, Directional compactness, scalarization and nonsmooth semi-Fredholm mappings, Nonlinear Anal. 29 (1997), 201-219. MR 98c:49043
6.: B. S. Mordukhovich, Coderivatives of set-valued mappings: calculus and applications, Nonlinear Anal. 30 (1997), 3059-3070.
7.: B. S. Mordukhovich and Y. Shao, Nonsmooth sequential analysis in Asplund spaces, Trans. Amer. Math. Soc. 348 (1996), 1235-1280. MR 96h:49036
8.: B. S. Mordukhovich and B. Wang, Restrictive metric regularity and generalized differential calculus in Banach spaces, preprint, Department of Mathematics, Wayne State University, 2002.
9.: R. T. Rockafellar, Maximal monotone relations and the second derivatives of nonsmooth functions, Ann. Inst. Henri Poincaré 2 (1985), 167-184. MR 87c:49021
10.: R. T. Rockafellar and R. J.-B. Wets, Variational Analysis, Springer, Berlin, 1998. MR 98m:49001
11.: L. Thibault, Sous-différentiel de fonctions vectorielles compactement lipschitziennes, C. R. Acad. Sc. Paris 286 (1978), 995-998. MR 80b:58014
12.: -, On compactly Lipschitzian mappings, Recent Advances in Optimization (P. Gritzmann et al., eds.), Lecture Notes in Econ. Math. Syst., Ser. 456, pp. 356-364, Springer, Berlin, 1997. MR 98f:49019

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 49J52, 58C20

Boris S. Mordukhovich
Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
Email: boris@math.wayne.edu

Bingwu Wang
Affiliation: Department of Mathematics, Eastern Michigan University, Ypsilanti, Michigan 48197
Email: wangbw@math.emich.edu

DOI: 10.1090/S0002-9939-02-06836-3
PII: S 0002-9939(02)06836-3
Keywords: Lipschitzian mappings, differentiability, Banach spaces, variational analysis, graphical regularity
Received by editor(s): March 23, 2001
Posted: September 25, 2002
Additional Notes: The first author was partly supported by the National Science Foundation under grants DMS-9704751 and DMS-0072179 and also by the Distinguished Faculty Fellowship at Wayne State University.
Communicated by: Jonathan M. Borwein
Copyright of article: Copyright 2002, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2008, American Mathematical Society Privacy Statement		Search the AMS