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A Limiting Example for the Local ``Fuzzy" Sum Rule in Nonsmooth Analysis

Vanderwerff, Jon D. and Zhu, Qiji J. (1996) A Limiting Example for the Local ``Fuzzy" Sum Rule in Nonsmooth Analysis. [Preprint]

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      Abstract

      We show that assuming all the summand functions to be lower semicontinuous is not sufficient to ensure a (strong) fuzzy sum rule for subdifferentials in any infinite dimensional Banach space. From this we deduce that additional assumptions are also needed on functions for chain rules, multiplier rules for constrained minimization problems and Clarke-Ledyaev type mean value inequalities in the infinite dimensional setting.

      Item Type: Preprint
      Additional Information: pubdom FALSE
      Subjects: 49-xx Calculus of variations and optimal control; optimization > 49Jxx Existence theories
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 28 Nov 2003
      Last Modified: 21 Apr 2010 11:13
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/177

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