Alternating Direction Method with Self-Adaptive Penalty Parameters for Monotone Variational Inequalities

By Bingsheng He, Hai Yang, Songhu Wang. 2000

458 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/82a6d3de3ac2eec2f3262b4b805514bdfa7b00b3

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In Computational Mechanics

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Citations in the corpus

Collaborative Sparse Regression for Hyperspectral Unmixing (2014, methodology): “For example, previous works [43], [44] (see also [45]) use an adaptive scheme (based on the primal and the dual ADMM variables) that performs very well in our case.”
Alternating direction augmented Lagrangian methods for semidefinite programming (2010, methodology): “Although the techniques for analyzing the alternating direction methods for variational inequalities in [15] and a class of nonlinear optimization problems in [1] can be applied to analyze our algorithm for SDPs in standard form, we present a different and simple convergence proof by formulating our”
Efficient Algorithms for Convolutional Sparse Representations (2016, methodology): “The other strategy is the adaptive method proposed in [50] and described in [3, Sec.”
Augmented Lagrangian alternating direction method for matrix separation based on low-rank factorization (2014, methodology): “The approach of ADM has been widely used in solving convex optimization and related problems, including problems arising from partial differential equations [21,24], variational inequality problems [27, 28], conic programming [15,42], various nonlinear convex programming [2,12,30,31,39], zerofinding”
A Fully Distributed Reactive Power Optimization and Control Method for Active Distribution Networks (2014, methodology): “VPP tuning techniques in existing literatures cannot work without central coordination [19], [20].”
Total Variation Spatial Regularization for Sparse Hyperspectral Unmixing (2012, methodology): “For example, previous work in [66], [67] (see also [68]) uses an adaptive scheme (based on the primal and the dual ADMM variables) that performs very well in our case.”
Decomposition Method with a Variable Parameter for a Class of Monotone Variational Inequality Problems (2001, background): “Assumption A2. The subvariational inequality (subVI) problem ( 12 ) is solvable.”
Adaptive Consensus ADMM for Distributed Optimization (2017, methodology): “In practice, however, the efﬁciency of ADMM is highly sensitive to this parameter choice (Nishihara et al., 2015; Ghadimi et al., 2015), and can be improved via adaptive penalty selection methods (He et al., 2000; Song et al., 2016; Xu et al., 2017a).”
Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization (2012, background): “We refer to, e.g., [23, 24, 27], for some self-adaptive rules of tuning β .”
A Field Guide to Forward-Backward Splitting with a FASTA Implementation (2014, background): “For other splitting methods, it is considerably more difficult to guarantee convergence for adaptive methods [54, 55].”
A Survey of Optimization Methods From a Machine Learning Perspective (2019, methodology): “peciﬁcally, an auto-adjustment criterion that automatically adjusts {βt}based on the current value of {xt} during the iteration was proposed, and applied for solving some convex optimization problems [115], [116]. The ADMM method uses the separable operators in the convex optimization problem to div”
Fast alternating linearization methods for minimizing the sum of two convex functions (2009, unknown): “ADMs have also been applied to solving variational inequality problems by Tseng [46, 47] and He et al. [24, 26].”
Fast and Accurate Matrix Completion via Truncated Nuclear Norm Regularization (2013, background): “As the choice of f kg is nondecreasing, the convergence of TNNR-ADMMAP is guaranteed by the theoretical result in [47].”