Differentiability and regularity of Lipschitzian mappings
HTML articles powered by AMS MathViewer
- by Boris S. Mordukhovich and Bingwu Wang PDF
- Proc. Amer. Math. Soc. 131 (2003), 389-399 Request permission
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.References
- Frank H. Clarke, Optimization and nonsmooth analysis, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, Inc., New York, 1983. A Wiley-Interscience Publication. MR 709590
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- Marián Fabián, Subdifferentiability and trustworthiness in the light of a new variational principle of Borwein and Preiss, Acta Univ. Carolin. Math. Phys. 30 (1989), no. 2, 51–56. 17th Winter School on Abstract Analysis (Srní, 1989). MR 1046445
- Aleksandr D. Ioffe, On subdifferentiability spaces, Fifth international conference on collective phenomena, Ann. New York Acad. Sci., vol. 410, New York Acad. Sci., New York, 1983, pp. 107–119. MR 775520, DOI 10.1111/j.1749-6632.1983.tb23308.x
- A. D. Ioffe, Directional compactness, scalarization and nonsmooth semi-Fredholm mappings, Nonlinear Anal. 29 (1997), no. 2, 201–219. MR 1446225, DOI 10.1016/S0362-546X(96)00046-6
- B. S. Mordukhovich, Coderivatives of set-valued mappings: calculus and applications, Nonlinear Anal. 30 (1997), 3059–3070.
- Boris S. Mordukhovich and Yong Heng Shao, Nonsmooth sequential analysis in Asplund spaces, Trans. Amer. Math. Soc. 348 (1996), no. 4, 1235–1280. MR 1333396, DOI 10.1090/S0002-9947-96-01543-7
- B. S. Mordukhovich and B. Wang, Restrictive metric regularity and generalized differential calculus in Banach spaces, preprint, Department of Mathematics, Wayne State University, 2002.
- R. T. Rockafellar, Maximal monotone relations and the second derivatives of nonsmooth functions, Ann. Inst. H. Poincaré Anal. Non Linéaire 2 (1985), no. 3, 167–184 (English, with French summary). MR 797269
- R. Tyrrell Rockafellar and Roger J.-B. Wets, Variational analysis, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 317, Springer-Verlag, Berlin, 1998. MR 1491362, DOI 10.1007/978-3-642-02431-3
- Lionel Thibault, Sous-différentiels de fonctions vectorielles compactement lipschitziennes, C. R. Acad. Sci. Paris Sér. A-B 286 (1978), no. 21, A995–A998 (French, with English summary). MR 497892
- Lionel Thibault, On compactly Lipschitzian mappings, Recent advances in optimization (Trier, 1996) Lecture Notes in Econom. and Math. Systems, vol. 452, Springer, Berlin, 1997, pp. 356–364. MR 1467041, DOI 10.1007/978-3-642-59073-3_{2}5
Additional Information
- Boris S. Mordukhovich
- Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
- MR Author ID: 215154
- ORCID: 0000-0002-3445-2406
- Email: boris@math.wayne.edu
- Bingwu Wang
- Affiliation: Department of Mathematics, Eastern Michigan University, Ypsilanti, Michigan 48197
- Email: wangbw@math.emich.edu
- Received by editor(s): March 23, 2001
- Published electronically: 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 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 389-399
- MSC (2000): Primary 49J52; Secondary 58C20
- DOI: https://doi.org/10.1090/S0002-9939-02-06836-3
- MathSciNet review: 1933329