Degenerate Nonlinear Programming with a Quadratic Growth Condition

By Mihai Anitescu. 1999

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Citations in the corpus

Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Łojasiewicz Condition (2016, background): “…of Luo and Tseng [1993], but four other recently-considered conditions are essential strong convexity (ESC) [Liu et al., 2014], weak strong convexity (WSC) [Necoara et al., 2015], the restricted secant inequality (RSI) [Zhang and Yin, 2013], and the quadratic growth (QG) condition [Anitescu, 2000].”
Asynchronous Stochastic Coordinate Descent: Parallelism and Convergence Properties (2014, background): “Lemma 4.6) is similar in that it requires a certain quantity to increase quadratically with distance from the solution set, but diﬀerent in that the objective is assumed to be diﬀerentiable. Anitescu [2] deﬁnes a “quadratic growth condition” for (smooth) nonlinear programming in which the objective ”
SGD for Structured Nonconvex Functions: Learning Rates, Minibatching and Interpolation (2020, background): “, 2019), the restricted secant inequality (Zhang and Yin, 2013), and the quadratic growth (QG) condition (Anitescu, 2000; Loizou, 2019).”
Constant-Rank Condition and Second-Order Constraint Qualification (2010, background): “As the example in [21] (rediscovered by Anitescu in [22]) shows, the MangasarianFromovitz constraint qualification is neither a strong nor a weak second-order constraint qualification.”
A Survey of the S-Lemma (2007, background): “Several other applications can be found in the literature, such as distance geometry [9], portfolio management [3, 4, 29], statistics [38], signal processing [50], and control and stability problems [11, 15, 53, 56], to mention just a few.”