Set-Valued Analysis

, Volume 11, Issue 1, pp 37–67 | Cite as

Local Lipschitz-constant Functions and Maximal Subdifferentials

  • J. M. Borwein
  • J. Vanderwerff
  • Xianfu Wang


It is shown that if k(x) is an upper semicontinuous and quasi lower semicontinuous function on a Banach space X, then k(x)BX* is the Clarke subdifferential of some locally Lipschitz function on X. Related results for approximate subdifferentials are also given. Moreover, on smooth Banach spaces, for every locally Lipschitz function with minimal Clarke subdifferential, one can obtain a maximal Clarke subdifferential map via its ‘local Lipschitz-constant’ function. Finally, some results concerning the characterization and calculus of local Lipschitz-constant functions are developed.

Lipschitz function Baire category Clarke subdifferential approximate subdifferential local Lipschitz-constant function 


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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • J. M. Borwein
    • 1
  • J. Vanderwerff
    • 2
  • Xianfu Wang
    • 3
  1. 1.Centre for Experimental and Constructive Mathematics, Department of Mathematics and StatisticsSimon Fraser UniversityBurnabyCanada
  2. 2.Department of Mathematics and ComputingLa Sierra UniversityRiversideU.S.A
  3. 3.Department of Mathematics and StatisticsOkanagan University CollegeKelownaCanada

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