Clarke subgradients of stratifiable functions

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dc.creatorBolte, J.
dc.creatorDaniilidis, A.
dc.creatorLewis, A. S.
dc.creatorShiota, M.
dc.date2006-01-22
dc.date.accessioned2026-07-07T06:59:10Z
dc.date.available2026-07-07T06:59:10Z
dc.descriptionWe establish the following result: if the graph of a (nonsmooth) real-extended-valued function $f:\mathbb{R}^{n}\to \mathbb{R}\cup\{+\infty\}$ is closed and admits a Whitney stratification, then the norm of the gradient of $f$ at $x\in{dom}f$ relative to the stratum containing $x$ bounds from below all norms of Clarke subgradients of $f$ at $x$. As a consequence, we obtain some Morse-Sard type theorems as well as a nonsmooth Kurdyka-Łojasiewicz inequality for functions definable in an arbitrary o-minimal structure.
dc.identifierhttps://arxiv.org/abs/math/0601530
dc.identifierhttp://arxiv.org/abs/math/0601530
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/107650
dc.subjectOptimization and Control
dc.subject49J52; 26D10; 32B20
dc.titleClarke subgradients of stratifiable functions
dc.typetext

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