Local Lipschitz-constant Functions and Maximal Subdifferentials

Set-Valued Analysis

Volumn 11, Issue 1, 2003, Pages 37-67

  Borwein, J M ^a   Vanderwerff, J ^b   Wang, Xianfu ^c  

^a SIMON FRASER UNIVERSITY   (Canada)

^b LA SIERRA UNIVERSITY   (United States)

^c OKANAGAN UNIVERSITY COLLEGE   (Canada)

Author keywords

Approximate subdifferential; Baire category; Clarke subdifferential; Lipschitz function; Local Lipschitz constant function

Indexed keywords

EID: 0037243339     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021975622768     Document Type: Article

References (19)

1. Benyamini, Y. and Lindenstrauss, J.: Geometric Nonlinear Functional Analysis, Vol. 1, Amer. Math. Soc. Colloq. Publ. 48, Amer. Math. Soc., Providence, RI, 2000.
2. Borwein, J. M.: Minimal CUSCOs and subgradients of Lipschitz functions, In: Fixed Point Theory and its Applications, Pitman Res. Notes 252, 1991, pp. 57-81.
3. Borwein, J. M. and Fitzpatrick, S.: Characterization of Clarke subgradients among one-dimensional multifunctions, In: B. M. Glover and V. Jeyakumar (eds), Proc. of the Optimization Miniconference 11, 1995, pp. 61-73.
4. Borwein, J. M. and Ioffe, A. D.: Proximal analysis in smooth spaces, Set-Valued Anal. 4 (1996), 1-24.
5. Borwein, J. M. and Moors, W. B.: Null sets and essentially smooth Lipschitz functions, SIAM J. Optim. 8 (1998), 309-323.
6. Borwein, J. M., Moors, W. B. and Wang, X.: Generalized subdifferentials: a Baire categorical approach, Trans. Amer Math. Soc. 353 (2001), 3875-3893.
7. Clarke, F. H.: Optimization and Nonsmooth Analysis, Wiley Interscience, New York, 1983.
8. Deville, R., Godefroy, G. and Zizler, V.: Smoothness and Renorming in Banach Spaces, Pitman Monogr. Surveys Pure Appl. Math. 64, Longman, Harlow, 1993.
9. Fitzpatrick, S.: Differentiability of real-valued functions and continuity of metric projections, Proc. Amer Math. Soc. 91 (1984), 544-548.
10. Giles, J. R.: Convex Analysis with Application in Differentiation of Convex Functions, Res. Notes Math. 58, 1982.
11. Ioffe, A. D.: Approximate subdifferentials and applications II, Mathematika 33 (1986), 111-128.
12. Ioffe, A. D.: Approximate subdifferentials and applications 3: the metric theory, Mathematika 36 (1989), 1-38.
13. Mordukhovich, B. S. and Shao, Y.: Nonsmooth sequential analysis in Asplund spaces, Trans. Amer Math. Soc. 348 (1996), 1235-1280.
14. Phelps, R. R.: Convex Functions, Monotone Operators and Differentiability, Lecture Notes in Math., Springer-Verlag Berlin Heidelberg, 1993.
15. Preiss, D., Phelps, R. R. and Namioka, I.: Smooth Banach spaces, weak Asplund spaces and monotone or usco mappings, Israel J. Math. 72 (1990), 257-279.
16. Preiss, D.: Differentiability of Lipschitz functions on Banach spaces, J. Funct. Anal. 91 (1990), 312-345.
17. Rockafellar, R. T. and Wets, R. J.-B.: Variational Analysis, Springer-Verlag, Berlin, 1998.
18. Stromberg, K. R.: An Introduction to Classical Real Analysis, Wadsworth International Mathematics Series, 1981.
19. Thibault, L.: On generalized differentials and subdifferentials of Lipschitz vector-valued functions, Nonlinear Anal. 6 (1982), 1037-1053.