A limiting example for the locall ``fuzzy'' sum rule in nonsmooth analysis
By J. Vanderwerff and Q. J. Zhu
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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