SEMIALGEBRAIC SARD THEOREM FOR GENERALIZED CRITICAL VALUES

By K. Kurdyka, P. Orro, S. Simon. 2000

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A nonsmooth Morse–Sard theorem for subanalytic functions (2006, background): “Existing deep results restrict attention to particular subclasses of functions (semialgebraic or “o-minimal,” for example) [3,6,10], distance functions to a manifold [17], or nonsmooth functions admitting a supremum representation [22], in order to relax the smoothness condition into simple differen”
Regularity at infinity of real mappings and a Morse–Sard theorem (2011, methodology): “In [15], Kurdyka, Orro and Simon considered C2 semi-algebraic maps f : Kn → Kp and a metric-type regularity condition which had been introduced by Rabier [23].”
Clarke Subgradients of Stratifiable Functions (2006, background): “Classical results deal with smooth functions [33], [22], but recent advances deal with a variety of nonsmooth settings [3], [13], [14], [15].”