Alternating direction augmented Lagrangian methods for semidefinite programming

By Zaiwen Wen, Donald Goldfarb, Wotao Yin. Mathematical Programming Computation, 2010

425 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/7dd48b100fc406da2a61117d5cbf15b046ce3468

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In Computational Mechanics

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Citations in the corpus

Multidimensional simultaneous random plus erratic noise attenuation and interpolation for seismic data by joint low-rank and sparse inversion (2015, methodology): “We propose to solve the resulting convex optimization problem for each temporal frequency slice with an efficient alternating direction method of multipliers (ADMM) scheme (Wen et al., 2010; Boyd et al., 2011; Tao and Yuan, 2011), which iteratively estimates and recovers the missing entries of the l”
Generalized approximate message passing for estimation with random linear mixing (2010, methodology): “In particular, the separable approximation method of [10] and alternating direction methods in [11]–[14] are all based on iterations of this form.”
Dropping Convexity for Faster Semi-definite Optimization (2015, methodology): “For linear f , we note among others the work of [76], a provably convergent alternating direction augmented Lagrangian algorithm, and that of Helmberg and Rendl [36], where they develop an eﬃcient ﬁrst-order spectral bundle method for SDPs with the constant trace property; see also [35] for…”
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”
Fast alternating linearization methods for minimizing the sum of two convex functions (2009, neutral): “This implies that (2.3) does not hold and hence, x k +1 := arg min x L µ ( x, y k ; λ k ), and the equivalence of Algorithms 3 and 4 follows.”
Proximal Algorithms (2013, methodology): “See [197] for a recent paper on applying ADMM to solving semidefinite programming problems.”
Operator Splitting for a Homogeneous Embedding of the Linear Complementarity Problem (2020, methodology): “Applying DR splitting to the embedded problem results in an iterative procedure with a per-iteration cost that is almost identical to the linear-convex case as tackled by SCS and to applying the splitting method directly to the original problem [75, 59].”
An alternating direction algorithm for matrix completion with nonnegative factors (2011, methodology): “In fact, the proposed algorithm in this paper extends the work in [34], and both algorithms are based on the algorithm of alternating direction method of multipliers (ADM) [12, 11, 2, 28, 32, 30].”
Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding (2013, methodology): “There are several different ways to apply ADMM to solve cone programs [8,13].”
The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent (2014, methodology): “We refer the reader to [10] for the analysis and [28] for some numerical experiments.”
Ieee Transactions on Pattern Analysis and Machine Intelligence Laplacian Regularized Low-rank Representation and Its Applications (neutral): “Algorithm 1: LADMAP for solving non-negative sparse Laplacian regularized LRR Input: Y , λ, β , γ and the number of nearest neighbors.”
Global Convergence of Splitting Methods for Nonconvex Composite Optimization (2014, positive): “This has been widely used recently; see, for example [10, 11, 33, 34, 36].”
Alternating Direction Algorithms for 1-Problems in Compressive Sensing (2009, methodology): “Recently, the ADM has also been applied to total variation based image reconstruction in [20, 52, 34] and to semi-definite programming in [49].”