Clarke Subgradients of Stratifiable Functions
نویسندگان
چکیده
منابع مشابه
Clarke Subgradients of Stratifiable Functions
We establish the following result: if the graph of a lower semicontinuous real-extendedvalued function f : Rn → R ∪ {+∞} admits a Whitney stratification (so in particular if f is a semialgebraic function), then the norm of the gradient of f at x ∈ dom f relative to the stratum containing x bounds from below all norms of Clarke subgradients of f at x. As a consequence, we obtain a Morse-Sard typ...
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Using a geometric argument, we show that under a reasonable continuity condition, the Clarke subdifferential of a semi-algebraic (or more generally stratifiable) directionally Lipschitzian function admits a simple form: the normal cone to the domain and limits of gradients generate the entire Clarke subdifferential. The characterization formula we obtain unifies various apparently disparate res...
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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2007
ISSN: 1052-6234,1095-7189
DOI: 10.1137/060670080