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Iteratively Linearized Reweighted Alternating Direction Method of Multipliers for a Class of Nonconvex Problems

Tao Sun, Hao Jiang, Lizhi Cheng, Wei Zhu
2018 IEEE Transactions on Signal Processing  
In view of this, we propose a reweighted alternating direction method of multipliers. In this algorithm, all subproblems are convex and easy to solve.  ...  The traditional alternating direction method of multipliers encounters troubles in both mathematics and computations in solving the nonconvex and nonsmooth subproblem.  ...  Conclusion In this paper, we consider a class of nonconvex and nonsmooth minimizations with linear constrains which have applications in signal processing and machine learning research.  ... 
doi:10.1109/tsp.2018.2868269 fatcat:eixcjm5kxbgvfbzjelaa42sadq

Iteratively reweighted penalty alternating minimization methods with continuation for image deblurring [article]

Tao Sun, Dongsheng Li, Hao Jiang, Zhe Quan
2019 arXiv   pre-print
In this paper, we consider a class of nonconvex problems with linear constraints appearing frequently in the area of image processing.  ...  We solve this problem by the penalty method and propose the iteratively reweighted alternating minimization algorithm.  ...  CONCLUSION In this paper, we propose an iteratively reweighted alternating minimization algorithm for a class of linearly constrained problems.  ... 
arXiv:1902.04062v1 fatcat:rmd75zhaezbozf4ytdpc2trufa

ADMM-IDNN: Iteratively Double-reweighted Nuclear Norm Algorithm for Group-prior based Nonconvex Compressed Sensing via ADMM [article]

Yunyi Li, Fei Dai, Yu Zhao, Xiefeng Cheng, Guan Gui
2020 arXiv   pre-print
To solve the resulting nonconvex nuclear norm minimization (NNM) problem, we develop a Group based iteratively double-reweighted nuclear norm algorithm (IDNN) via an alternating direction method of multipliers  ...  Our proposed algorithm can convert the nonconvex nuclear norms optimization problem into a double-reweighted singular value thresholding (DSVT) problem.  ...  Acknowledge The authors would like to thank Associate Editor for his efforts in coordinating the review of our manuscript, and thank three anonymous reviewers for their constructive suggestions to improve  ... 
arXiv:1903.09787v4 fatcat:ekdvklhyzzdlzn6lfkpm67ws2u

Distributed Reconstruction of Nonlinear Networks: An ADMM Approach [article]

Wei Pan, Aivar Sootla, Guy-Bart Stan
2014 arXiv   pre-print
To this end, we apply the alternating direction method of multipliers (ADMM) to decompose the original problem into several subproblems.  ...  Using a convex-concave procedure (CCCP), an iterative reweighted lasso algorithm was derived to solve the initial nonconvex optimisation problem.  ...  ALTERNATING DIRECTION METHOD OF MULTIPLIERS (ADMM) In this section we give an overview of ADMM.  ... 
arXiv:1403.7429v1 fatcat:rk2gjf2bgjgbfpefzb6q7ghp5e

Distributed Reconstruction of Nonlinear Networks: An ADMM Approach

Wei Pan, Aivar Sootla, Guy-Bart Stan
2014 IFAC Proceedings Volumes  
To this end, we apply the alternating direction method of multipliers (ADMM) to decompose the original problem into several subproblems.  ...  In this paper, we derive an iterative reweighted lasso algorithm to solve the initial nonconvex optimisation problem based on the concave-convex procedure (CCCP).  ...  Here, we will apply the alternating direction method of multipliers (ADMM) to split the centralised problem into several subproblems with each subproblem solving a weighed lasso problem independently.  ... 
doi:10.3182/20140824-6-za-1003.02602 fatcat:xtr7seefqzcnliqumwtzc7rodq

A Nonconvex Implementation of Sparse Subspace Clustering: Algorithm and Convergence Analysis

Xiaoge Deng, Tao Sun, Peibing Du, Dongsheng Li
2020 IEEE Access  
However, this formulation makes the optimization task challenging due to that the traditional alternating direction method of multipliers (ADMM) encounters troubles in solving the nonconvex subproblems  ...  Experiments on two real-world problems of motion segmentation and face clustering show that our method outperforms state-of-the-art techniques.  ...  Although the optimization problem of the q,ε -norm constraint is nonconvex, a reweighted alternating direction method of multipliers algorithm is designed for the nonconvex subproblem, then the problem  ... 
doi:10.1109/access.2020.2981740 fatcat:6rpxuu275fgabjg2ge6rln4k5m

Sparsity-aware field estimation via ordinary Kriging

Sijia Liu, Engin Masazade, Makan Fardad, Pramod K. Varshney
2014 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
To solve the proposed non-convex optimization problem, we employ the alternating direction method of multipliers (ADMM) and the reweighted 1 minimization method, respectively.  ...  In this paper, we consider the problem of estimating a spatially varying field in a wireless sensor network, where resource constraints limit the number of sensors selected in the network that provide  ...  However, it has been recently observed in [10] - [13] that the alternating direction method of multipliers (ADMM) is a powerful tool in solving optimization problems that include cardinality functions  ... 
doi:10.1109/icassp.2014.6854342 dblp:conf/icassp/LiuMFV14 fatcat:xl7et57jvveqbiqnphervvlbca

Convex Total Least Squares [article]

Dmitry Malioutov, Nikolai Slavov
2014 arXiv   pre-print
To solve such problems, we develop convex relaxation approaches for a general class of structured TLS (STLS).  ...  We describe a fast solution based on augmented Lagrangian formulation, and apply our approach to an important class of biological problems that use population average measurements to infer cell-type and  ...  This is closely related to the popular alternating direction of multipliers methods (Boyd et al., 2011) .4 For many constraints of interest this projection is highly efficient: when the constraint fixes  ... 
arXiv:1406.0189v1 fatcat:cufijza2yvhxxbbfgy36kllibu

An Alternating Proximal Splitting Method with Global Convergence for Nonconvex Structured Sparsity Optimization

Shubao Zhang, Hui Qian, Xiaojin Gong
In this paper, we propose a splitting method for solving nonconvex structured sparsity optimization problems.  ...  The proposed method alternates between a gradient step and an easily solvable proximal step, and thus enjoys low per-iteration computational complexity.  ...  ADMM: The alternating direction method of multipliers for solving the overlappling group lasso problem (13) (Deng, Yin, and Zhang 2011) .  ... 
doi:10.1609/aaai.v30i1.10253 fatcat:euw72mz7zraxtlunlf2vyyql5y

On the design of optimal structured and sparse feedback gains via sequential convex programming

Makan Fardad, Mihailo R. Jovanovic
2014 2014 American Control Conference  
Via linearizations of the nonconvex constraint, we introduce an iterative algorithm that solves a semidefinite program at every stage and for which the nonconvex constraint is satisfied upon convergence  ...  We elaborate on the modular nature of the proposed scheme and show that it can be used in a wide range of network control problems.  ...  Optimal Sparse Feedback Gains The problem of designing sparse feedback gains was considered in [3] , [4] , [19] , where the alternating direction method of multipliers and reweighted 1 relaxations were  ... 
doi:10.1109/acc.2014.6859120 dblp:conf/amcc/FardadJ14 fatcat:vu3vsx2hrrffjn6nmbrvhihhyu

Enhancing Sparsity by Reweighted ℓ 1 Minimization

Emmanuel J. Candès, Michael B. Wakin, Stephen P. Boyd
2008 Journal of Fourier Analysis and Applications  
The algorithm consists of solving a sequence of weighted ℓ 1 -minimization problems where the weights used for the next iteration are computed from the value of the current solution.  ...  In this paper, we study a novel method for sparse signal recovery that in many situations outperforms ℓ 1 minimization in the sense that substantially fewer measurements are needed for exact recovery.  ...  C. was partially supported by a National Science Foundation grant CCF-515362, by the 2006 Waterman Award (NSF) and by a grant from DARPA. This work was performed while M.  ... 
doi:10.1007/s00041-008-9045-x fatcat:nsmi6aeqazebjdvwvm72ro6c4m

Generalized Nonconvex Nonsmooth Low-Rank Minimization

Canyi Lu, Jinhui Tang, Shuicheng Yan, Zhouchen Lin
2014 2014 IEEE Conference on Computer Vision and Pattern Recognition  
Based on this property, we propose an Iteratively Reweighted Nuclear Norm (IRNN) algorithm to solve the nonconvex nonsmooth low-rank minimization problem.  ...  IRNN iteratively solves a Weighted Singular Value Thresholding (WSVT) problem.  ...  Lin is supported by NSF of China (Grant nos. 61272341, 61231002, and 61121002) and M-SRA.  ... 
doi:10.1109/cvpr.2014.526 dblp:conf/cvpr/LuTYL14 fatcat:z7mlvanz2fhzzpighdwvylzada

Performance evaluation of typical approximation algorithms for nonconvex ℓ_p-minimization in diffuse optical tomography

Calvin B. Shaw, Phaneendra K. Yalavarthy
2014 Optical Society of America. Journal A: Optics, Image Science, and Vision  
In this work, three such typical methods for implementing the l p -norm were considered, namely, iteratively reweighted l 1 -minimization (IRL1), iteratively reweighted least squares (IRLS), and the iteratively  ...  These methods were deployed for performing diffuse optical tomographic image reconstruction, and a systematic comparison with the help of three numerical and gelatin phantom cases was executed.  ...  The minimization scheme deployed in SALSA makes use of a variable splitting, which is achieved using an alternating direction method of multipliers (ADMM).  ... 
doi:10.1364/josaa.31.000852 pmid:24695149 fatcat:ugr344b5ijhjvgkpupnmsydsqa

Efficient Outlier Removal in Large Scale Global Structure-from-Motion [article]

Fei Wen, Danping Zou, Rendong Ying, Peilin Liu
2019 arXiv   pre-print
The first method considers a convex relaxed ℓ_1 minimization and is solved by a single linear programming (LP), whilst the second one approximately solves the ideal ℓ_0 minimization by an iteratively reweighted  ...  The dimension reduction results in a significant speedup of the new algorithms. Further, the iteratively reweighted method can significantly reduce the possibility of removing true inliers.  ...  These methods reformulate the consensus maximization problem with linear complementarity constraints, and employ the Frank-Wolfe optimization scheme and alternating direction method of multipliers (ADMM  ... 
arXiv:1808.03041v4 fatcat:eyu6yvgpunf5zgnixtl6ywr334

Continuous Relaxation of MAP Inference: A Nonconvex Perspective

D. Khue Le-Huu, Nikos Paragios
2018 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition  
direction method of multipliers (ADMM).  ...  In addition, we study the resolution of this relaxation using popular gradient methods, and further propose a more effective solution using a multilinear decomposition framework based on the alternating  ...  The authors thank Jean-Christophe Pesquet for useful discussion on gradient-based methods, and thank the anonymous reviewers for their insightful comments.  ... 
doi:10.1109/cvpr.2018.00580 dblp:conf/cvpr/Le-HuuP18 fatcat:s2bofb52kfbvdbhbdaxfqs26zm
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