Abstract
In terms of Baire category, a typical real-valued Lipschitz function on a finite dimensional space has a local minimum at every point of a dense subset of the domain, and a Dini subdifferential that is either singleton or empty at all points. Moreover, its Dini subdifferential is empty outside a set of first category. Hence a typical Lipschitz function has no points of subdifferential regularity.
Citation
Philip D. Loewen. Xianfu Wang. "Typical Properties of Lipschitz Functions." Real Anal. Exchange 26 (2) 717 - 726, 2000/2001.
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