A nonsmooth Morse-Sard theorem for subanalytic functions
نویسندگان
چکیده
According to the Morse-Sard theorem, any sufficiently smooth function on a Euclidean space remains constant along any arc of critical points. We prove here a theorem of Morse-Sard type suitable as a tool in variational analysis: we broaden the definition of a critical point to the standard notion in nonsmooth optimization, while we restrict the functions under consideration to be semi-algebraic or subanalytic. We make no assumption of subdifferential regularity. Ã Lojasiewicz-type inequalities for nonsmooth functions follow quickly from tools of the kind we develop, leading to convergence theory for subgradient dynamical systems.
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