Error bounds for analytic systems and their applications

By Zhi-Quan Tom Luo, Jong-Shi Pang. 1994

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Citations in the corpus

Analysis of classifiers’ robustness to adversarial perturbations (2015, background): “For example, Lojasiewicz (Łojasiewicz, 1961) and later (Luo and Pang, 1994) have shown that, quite remarkably, assumption (A) holds for the general class of analytic functions.”
New fractional error bounds for polynomial systems with applications to Hölderian stability in optimization and spectral theory of tensors (2015, methodology): “Furthermore, it is stated by the authors of [36] in their concluding remarks that “we have not been able to obtain explicit formulas for the multiplier or the exponent in the error bound.”
From error bounds to the complexity of first-order descent methods for convex functions (2015, methodology): “Key words: Error bounds, convex minimization, forward-backward method, KL inequality, complexity of first-order methods, LASSO, compressed sensing.”
Error Bounds for Convex Inequality Systems (1998, methodology): “2 in [27], for every compact set T Mn, there exist positive scalars 0 and 0 such that for all X 2 T , dist(X; C \Mn+) 0 [max(maxf(gi(X))+ : i = 1; : : : ; mg; maxf(det(X )) : Ng ) ] 0 : Since T is compact and gi is analytic, it follows that there exists a positive constant L > 0 such that for all X ”
Convergence of the Iterates of Descent Methods for Analytic Cost Functions (2005, methodology): “The latter result has been used in the study of error bounds of analytic inequality systems in optimization [27, 9].”
A Conditional Gradient-based Method for Simple Bilevel Optimization with Convex Lower-level Problem (2022, background): “…bound condition in (11) is well-studied in the optimization literature (see (Pang, 1997; Bolte et al., 2017; Roulet and d’Aspremont, 2020) and the references therein) and is known to hold generally when the function g is analytic and the set Z is bounded (Łojasiewicz, 1959; Luo and Pang, 1994).”