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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