Bull. Austral. Math. Soc. 72(3) pp.491--496, 2005.
Lipschitz functions with maximal Clarke subdifferentials are staunch
Jonathan M. Borwein
Research for the first author was supported by NSERC and
the CRC programme.
Research for the second author was supported by NSERC.
In a recent paper we have shown that most non-expansive Lipschitz functions (in the sense of Baire's category) have a maximal Clarke subdifferential. In the present paper, we show that in a separable Banach space the set of non-expansive Lipschitz functions with a maximal Clarke subdifferential is not only of generic, but also staunch.
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|(Metadata: XML, RSS, BibTeX)||MathSciNet: MR2199651||Z'blatt-MATH: 1121.49015|
- J.M. Borwein and X. Wang;
Lipschitz functions with maximal subdifferentials are generic,
Proc. Amer. Math. Soc. 128 (2000), pp. 3221--3229. MR1777577
- J.M. Borwein, W.B. Moors and X. Wang;
Generalized subdifferentials: a Baire categorical approach,
Trans. Amer. Math. Soc. 353 (2001), pp. 3875--3893. MR1837212
- F.H. Clarke;
Optimization and nonsmooth analysis (Wiley Interscience, New York, 1983). MR709590
- J.R. Giles and S. Sciffer;
Locally Lipschitz functions are generically pseudo-regular on separable Banach spaces,
Bull. Austral. Math. Soc. 47 (1993), pp. 205--212. MR1210135
- S. Reich, A.J. Zaslavski;
The set of noncontractive mappings is σ-porous in the space of all non-expansive mappings,
C. R. Acad. Sci. Paris 333 (2001), pp. 539--544. MR1860926
- L. Zajicek;
Small non-σ-porous sets in topologically complete metric spaces,
Colloq. Math. 77 (1998), pp. 293--304. MR1628994