A Primer on Monotone Operator Methods

By Ernest K. Ryu, Stephen P. Boyd. 2015

386 citations recorded by the source corpus.

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In Optimization & Training

Citations in the corpus

Frank-Wolfe Splitting via Augmented Lagrangian Method (2018, background): “the recent reviews (Glowinski et al., 2017; Ryu and Boyd, 2016), which cover the more general proximal splitting framework).”
Batch Stationary Distribution Estimation (2020, methodology): “To control the error due to sampling, we introduce a damped version of the update (Ryu and Boyd, 2016), where instead of performing a stochastic update ⌧ t +1 = T p p ⌧ t , we instead perform a damped update given by where ↵ t 2 (0 , 1) is a stepsize parameter.”
Stochastic Variance Reduction Methods for Saddle-Point Problems (2016, positive): “However, it turns out that our algorithm and, more importantly, our analysis extend to all set-valued monotone operators [8, 28].”
Plug-and-Play Methods Provably Converge with Properly Trained Denoisers (2019, background): “Lemma 7 is proved in a weaker form as Theorem 3 of (Polyak, 1987) and in Section 5.1 of (Ryu & Boyd, 2016).”
FedSplit: An algorithmic framework for fast federated optimization (2020, background): “Methods for solving monotone inclusions have a long history of study within the applied mathematics and optimization literatures [28, 7].”
Proximal Splitting Algorithms: A Tour of Recent Advances, with New Twists. (2020, background): “For more notions of convex analysis and operator theory, we refer the reader to the textbooks [24, 25] or to the papers [17,26].”
Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks (2019, background): “By the left inequality, the operator φ(x) is strongly monotone with parameter α [32], or equivalently the anti-derivative function ∫ φ(x)dx is strongly convex with parameter α.”
Operator Splitting for a Homogeneous Embedding of the Linear Complementarity Problem (2020, methodology): “The resulting embedded problem can be expressed as ﬁnding a zero of the sum of two maximal monotone operators, to which we can apply standard operator splitting methods [7, 65].”