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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Lipschitz functions with maximal Clarke subdifferentials are generic


Authors: Jonathan M. Borwein and Xianfu Wang
Journal: Proc. Amer. Math. Soc. 128 (2000), 3221-3229
MSC (1991): Primary 49J52; Secondary 26E25, 54E52
Published electronically: July 6, 2000
MathSciNet review: 1777577
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Abstract:

We show that on a separable Banach space most Lipschitz functions have maximal Clarke subdifferential mappings. In particular, the generic nonexpansive function has the dual unit ball as its Clarke subdifferential at every point. Diverse corollaries are given.


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Additional Information

Jonathan M. Borwein
Affiliation: Centre for Experimental and Constructive Mathematics, Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
Email: jborwein@cecm.sfu.ca

Xianfu Wang
Affiliation: Centre for Experimental and Constructive Mathematics, Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
Email: xwang@cecm.sfu.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05914-1
PII: S 0002-9939(00)05914-1
Keywords: Lipschitz function, Clarke subdifferential, separable Banach spaces, Baire category, partial ordering, Banach lattice, approximate subdifferential
Received by editor(s): September 28, 1998
Published electronically: July 6, 2000
Additional Notes: The first author’s research was supported by NSERC and the Shrum endowment of Simon Fraser University.
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society