Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité d'une classe de problèmes de Dirichlet non linéaires

By R. Glowinski, A. Marroco. 1975

Subfields: Numerical Methods & Scientific Computing

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Citations in the corpus

Frank-Wolfe Splitting via Augmented Lagrangian Method (2018, methodology): “One of the most popular algorithms in this framework is the alternating direction method of multipliers ( ADMM ), proposed by Glowinski and Marroco (1975), studied by Gabay and Mercier (1976), and revisited many times; see for instance (Boyd et al., 2011; Yan and Yin, 2016).”
GADMM: Fast and Communication Efficient Framework for Distributed Machine Learning (2019, methodology): “First, Gauss-Seidel ADMM yields the convergence rate o (1 /k ) (Glowinski and Marroco, 1975).”
A Primer on Monotone Operator Methods (2015, background): “One approach avoids discussing monotone operators and relies on first principles [56, 49, 17].”
APPROXIMATION OF A NONLINEAR ELLIPTIC PROBLEM ARISING IN A NON-NEWTONIAN FLUID FLOW MODEL IN GLACIOLOGY (2003, unknown): “(26) Let us remark that with the same techniques used in Glowinski–Marrocco [6] for the p-Laplacian problem with p = 2 − α, we can prove that function f given by (3) satisfies the two following inequalities: 〈f (|ξ|) ξ − f (|η|) η, ξ − η〉 ≥ χ min ( |ξ|−α , |η|−α , 1 ) .”
Differentiable Causal Discovery Under Latent Interventions (2022, methodology): “…enables formulating causal discovery under latent interventions as the following optimization problem: Following Zheng et al. (2018), we use the augmented Lagrangian (AL) method (Hestenes, 1969; Powell, 1969; Glowinski and Marroco, 1975) to address this problem via a sequence of unconstrained ones.”
An introduction to continuous optimization for imaging (2016, methodology): “…now commonly referred to as ‘proximal splitting’ and, although it relies on ideas from as far back as the 1950s or 1970s (Douglas and Rachford 1956, Glowinski and Marroco 1975), it has been a very active topic in the past ten years in image and signal processing, as well as in statistical…”
Fast ℓ1-minimization algorithms and an application in robust face recognition: A review (2010, background): “ADM can be attributed to the early works of [22], [21].”
Hinge-Loss Markov Random Fields and Probabilistic Soft Logic (2015, methodology): “…enables us to relax the equality constraints y (L,̂i) = y (C,̂i) in order to divide problem (45) into independent subproblems that are easier to solve, using the alternating direction method of multipliers (ADMM) (Glowinski and Marrocco, 1975; Gabay and Mercier, 1976; Boyd et al., 2011).”
Tensor completion and low-n-rank tensor recovery via convex optimization (2011, unknown): “ADM goes back to the seventies [21, 22] It is known that ADM is an application of the Douglas-Rachford splitting to the dual problem of the minimization of (f + g)(x) [23, 24].”
Proximal Splitting Algorithms: A Tour of Recent Advances, with New Twists. (2020, methodology): “The Alternating Direction Method of Multipliers (ADMM) goes back to Glowinski and Marocco [65], and Gabay and Mercier [66].”
Walkman: A Communication-Efficient Random-Walk Algorithm for Decentralized Optimization (2018, methodology): “Walkman can be derived by modifying existing algorithms to use a random walk, for example, ADMM [31], [32] or PPG [33].”
Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing (2010, unknown): “The proposed algorithms are based on the alternating direction method of multipliers (ADMM) [9, 8, 7], which decomposes a difﬁcult problem into a sequence of simpler ones.”
Guaranteed and robust a posteriori error estimates and balancing discretization and linearization errors for monotone nonlinear problems (2011, methodology): “The function a in the deﬁnition (1.2) of the ﬂux function σ is assumed to satisfy the following growth condition : There are constants R 1 , c 1 , and c 2 such that for all x ≥ R 1 , (2.2) Owing to the upper bound in (2.2) and using the H¨older inequality, it is readily seen that for all u ∈ V , σ…”