Sur le problème de la division

By S. Łojasiewicz. 1959

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Analysis of classifiers’ robustness to adversarial perturbations (2015, methodology): “an be used to bound the distance from xto a datapoint yclassiﬁed 1 (resp. 1). Bounds of the form Eq. (6) have been established for various classes of functions since the early of work of Lojasiewicz (Łojasiewicz, 1961) in algebraic geometry and have found applications in areas such as mathematical o”
Stabilisation of infinitesimally rigid formations of multi-robot networks (2009, background): “One way to do this is to exploit properties of gradient systems (Lojawiewicz 1959).”
Convergence of the Iterates of Descent Methods for Analytic Cost Functions (2005, background): “4The Lojasiewicz gradient inequality is a special instance of a more general Lojasiewicz inequality [23, 26].”
Convergence versus integrability in Birkhoff normal form (2001, background): “In particular, we have the following Lojasiewicz inequality (see [13]): there exist a positive number N and a positive constant C such that”
Error Bounds: Necessary and Sufficient Conditions (2010, background): “Since the fundamental works of Hoffman [21] and Lojasiewicz [36], the notion of (local) error bound plays a key role in variational analysis.”