A regularized alternating direction method of multipliers for a class of nonconvex problems

Jian, Jinbao; Zhang, Ye; Chao, Mian Tao

doi:10.1186/s13660-019-2145-0

Cited by 4 publications

(4 citation statements)

References 23 publications

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“…In the following, we compare Algorithm 1.1 with the regularized ADMM (RADMM, [26]) for solving two different cases of the sparse signal recovery problem:…”

Section: Comparative Experimentsmentioning

confidence: 99%

“…We also apply the Bregman modification of ADMM (BADMM, [39]) and the symmetric ADMM (SADMM, [41]) to solve the problems (1.2) and (1.3) by introducing auxiliary variable y = x for the sparse objective function. The proximal matrix in [26] is G = αI − βA T A, where (α, β) = (2.5, 0.12). The Bregman distance and related parameters of [39] use the default settings as mentioned therein, while the penalty parameter is set as 0.15 since it performs better 1) Note that this is also a special case of (1.1) with f (x) = µ x 1 , g(y) = y − c 2 /2, B = −I and b = 0. than using the value 10.…”

Section: Comparative Experimentsmentioning

confidence: 99%

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Accelerated Symmetric ADMM and Its Applications in Large-Scale Signal Processing

Bai,

Guo,

Liang

et al. 2024

JCM

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The alternating direction method of multipliers (ADMM) has been extensively investigated in the past decades for solving separable convex optimization problems, and surprisingly, it also performs efficiently for nonconvex programs. In this paper, we propose a symmetric ADMM based on acceleration techniques for a family of potentially nonsmooth and nonconvex programming problems with equality constraints, where the dual variables are updated twice with different stepsizes. Under proper assumptions instead of the socalled Kurdyka-Lojasiewicz inequality, convergence of the proposed algorithm as well as its pointwise iteration-complexity are analyzed in terms of the corresponding augmented Lagrangian function and the primal-dual residuals, respectively. Performance of our algorithm is verified by numerical examples corresponding to signal processing applications in sparse nonconvex/convex regularized minimization.

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“…In the following, we compare Algorithm 1.1 with the regularized ADMM (RADMM, [26]) for solving two different cases of the sparse signal recovery problem:…”

Section: Comparative Experimentsmentioning

confidence: 99%

Section: Comparative Experimentsmentioning

confidence: 99%

Accelerated Symmetric ADMM and Its Applications in Large-Scale Signal Processing

Bai,

Guo,

Liang

et al. 2024

JCM

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“…is widespread application has sparked a strong interest in further understanding the theoretical nature of the ADMM (see [14][15][16][17]).…”

Section: Introductionmentioning

confidence: 99%

Alternating Direction Multiplier Method for Matrix l2,1-Norm Optimization in Multitask Feature Learning Problems

Liu

Wang

2020

Mathematical Problems in Engineering

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The joint feature selection problem can be resolved by solving a matrix l2,1-norm minimization problem. For l2,1-norm regularization, one of the most fascinating features is that some similar sparsity structures can be employed by multiple predictors. However, the nonsmooth nature of the problem brings great challenges to the problem. In this paper, an alternating direction multiplier method combined with the spectral gradient method is proposed for solving the matrix l2,1-norm optimization problem involved with multitask feature learning. Numerical experiments show the effectiveness of the proposed algorithm.

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“…Combining the Bregman distance, Wang et al [31] obtained the convergence of Bregman ADMM in nonconvex multi-block case. For more research on multi-block splitting methods, see [21,33,34,35,36] and related references.…”

mentioning

confidence: 99%

Convergence analysis of an ALF-based nonconvex splitting algorithm with SQP structure

Liu¹,

Shao²,

Long³

et al. 2023

JIMO

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<p style='text-indent:20px;'>In this paper, by combining the splitting method of augmented Lagrange function (ALF) with the sequential quadratic programming (SQP) approximation, a novel ALF-based splitting algorithm with SQP structure is proposed for multi-block linear constrained nonconvex separable optimization. The new algorithm uses ALF-based splitting idea to decompose the original problem into several small-scale subproblems. Meanwhile, the SQP approximation and Armijo-type line search are used to solve some subproblems with smoothness concurrently. Under the conventional weak hypothesis, the decreasing property of ALF as merit function is obtained. Furthermore, the global convergence, strong convergence and convergence rate results of the new algorithm in general sense are given.</p>

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A regularized alternating direction method of multipliers for a class of nonconvex problems

Cited by 4 publications

References 23 publications

Accelerated Symmetric ADMM and Its Applications in Large-Scale Signal Processing

Accelerated Symmetric ADMM and Its Applications in Large-Scale Signal Processing

Alternating Direction Multiplier Method for Matrix l2,1-Norm Optimization in Multitask Feature Learning Problems

Convergence analysis of an ALF-based nonconvex splitting algorithm with SQP structure

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