A limiting example for the local “fuzzy” sum rule in nonsmooth analysis

Vanderwerff, Jon; Zhu, Qiji

doi:10.1090/S0002-9939-98-04365-2

A limiting example for the local “fuzzy” sum rule in nonsmooth analysis
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by Jon Vanderwerff and Qiji J. Zhu

Proc. Amer. Math. Soc. 126 (1998), 2691-2697

DOI: https://doi.org/10.1090/S0002-9939-98-04365-2

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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.

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