Set-Valued Analysis

, Volume 4, Issue 1, pp 1–24 | Cite as

Proximal analysis in smooth spaces

  • Jonathan M. Borwein
  • Alexander Ioffe


We provide a highly-refined sequential description of the generalized gradients of Clarke and approximate G-subdifferential of a lower semicontinuous extended-real-valued function defined on a Banach space with a β-smooth equivalent renorm. In the case of a Fréchet differentiable renorm, we give a corresponding result for the corresponding singular objects.

Mathematics Subject Classifications (1991)

Primary: 49J52 Secondary: 49J50, 58C20 

Key words

Lipschitz functions lower semi-continuous functions sub-derivatives variational principles distance functions tangent cones normals smooth renorms Clarke-subdifferentials G-subdifferentials 


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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Jonathan M. Borwein
    • 1
  • Alexander Ioffe
    • 2
  1. 1.Department of Mathematics and StatisticsSimon Fraser UniversityBurnabyCanada
  2. 2.Department of MathematicsTechnion-Israel Institute of TechnologyHaifaIsrael

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