A new inexact alternating directions method for monotone variational inequalities

By Bingsheng He, L. Liao, Deren Han, Hai Yang. Mathematical programming, 2002

473 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/f045b3e4f4a4e043b47600ae81c5cea6f7bae461

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Xiaoming Yuan
2. Yin Zhang
3. Junfeng Yang
4. Wotao Yin
5. Zaiwen Wen
6. Ting Kei Pong
7. Yuan Shen
8. Bingsheng He

In Control and Systems Engineering

1. Xiaoming Yuan
2. Wotao Yin
3. Junfeng Yang
4. Yin Zhang
5. Zaiwen Wen
6. Juan Peypouquet
7. Wei Deng
8. Min Tao

In Numerical Analysis

1. Wotao Yin
2. Yin Zhang
3. Xiaoming Yuan
4. Zaiwen Wen
5. Junfeng Yang
6. Ting Kei Pong
7. Paul Tseng
8. Yuan Shen

Citations in the corpus

• Hankel Matrix Rank Minimization with Applications to System Identification and Realization (2013, methodology): “The convergence results provided in [14] and [25] for the proximal ADM both need S and T to be positive definite, which limits the applications of the method.”
• Convex Optimization in Normed Spaces: Theory, Methods and Examples (2015, background): “This approach has been followed by [15], [103] and [38] (see also [52], [62] and [37]).”
• A Fast Alternating Direction Method for TVL1-L2 Signal Reconstruction From Partial Fourier Data (2010, methodology): “Moreover, the ADM has been extended to inexact minimization of subproblems; see [23] and [33].”
• 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”
• ADMM Based Privacy-Preserving Decentralized Optimization (2017, methodology): “= lim k→∞ (‖ λ − λ∗ ‖2(ρk+1)−1 + ‖ x k+1 − x∗ ‖2Q̄−ATρk+1A) ≥ 0 (46) Since α is positive and bounded and ‖ Ax ‖(2)ρi + ‖ x − x ‖2−ATρiA+Q̄ is nonnegative, following Theorem 3 in [46], we have”
• On the Global and Linear Convergence of the Generalized Alternating Direction Method of Multipliers (2016, methodology): “The proof steps are similar to the existing ADM convergence theory in [23,37] but are adapted to Algorithm 2.”
• Sparse and low-rank matrix decomposition via alternating direction method (2013, methodology): “We refer to the wide applications of ADM in many areas such as convex programming, variational inequalities and image processing, see, e.g., [2] [7] [12] [13] [18] [19] [20] [21] [22] [24] [28] [39].”
• Improving the Privacy and Accuracy of ADMM-Based Distributed Algorithms (2018, background): “For instance, (He et al., 2002; Magn´usson et al., 2014; Aybat & Iyengar, 2015; Xu et al., 2016) vary this penalty parameter in every iteration but keep it the same for different equality constraints in (2).”
• Alternating Direction Algorithms for 1-Problems in Compressive Sensing (2009, background): “On the other hand, the analysis in [31] does cover the convergence of (2.13) but only for the case γ = 1.”
• Alternating direction augmented Lagrangian methods for semidefinite programming (2010, methodology): “This simple idea has been applied to many other problem classes, such as, variational inequality problems [14, 15], linear programming [9], nonlinear convex optimization [1, 19, 7, 18, 26], maximal monotone operators [10] and nonsmooth l1 minimization arising from compressive sensing [28, 32, 34].”
• Convergence Analysis of Primal-Dual Algorithms for a Saddle-Point Problem: From Contraction Perspective (2012, background): “Note that (2.3) can be regarded as the PPA with a preconditioning proximal term (see, e.g., [11]) or the PPA in the context of the G -norm (defined by (cid:2) u (cid:2) G = √ u T Gu ) [11, 17].”
• Convex Optimization in Normed Spaces (2015, background): “This approach has been followed by [15], [103] and [38] (see also [52], [62] and [37]).”
• Recovering Low-Rank and Sparse Components of Matrices from Incomplete and Noisy Observations (2011, methodology): “Recall that the ADM dates back to [23] [24] [25] [26] and is closely related to the Douglas-Rachford operator splitting method [12]; and it has attracted wide attention of many authors in various areas, see e.g. [3] [10] [14] [15] [22] [29] [31] [36] [49] [50].”