966
Views
61
CrossRef citations to date
0
Altmetric
Original Articles

Convergence of alternating direction method for minimizing sum of two nonconvex functions with linear constraints

, &
Pages 1653-1669 | Received 31 May 2015, Accepted 18 May 2016, Published online: 03 Sep 2016

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (4)

Xiaoquan Wang, Hu Shao, Pengjie Liu & Wenli Yang. (2023) An inertial proximal splitting method with applications. Optimization 0:0, pages 1-30.
Read now
M. T. Chao, Y. Zhang & J. B. Jian. (2021) An inertial proximal alternating direction method of multipliers for nonconvex optimization. International Journal of Computer Mathematics 98:6, pages 1199-1217.
Read now
Max L. N. Gonçalves, Jefferson G. Melo & Renato D. C. Monteiro. (2020) On the iteration-complexity of a non-Euclidean hybrid proximal extragradient framework and of a proximal ADMM. Optimization 69:4, pages 847-873.
Read now
Yue Lu, Ming Huang, Yi Zhang & Jian Gu. (2019) A nonconvex ADMM for a class of sparse inverse semidefinite quadratic programming problems. Optimization 68:6, pages 1075-1105.
Read now

Articles from other publishers (57)

Kunyu Zhang, Hu Shao, Ting Wu & Xiaoquan Wang. (2024) A class of accelerated GADMM-based method for multi-block nonconvex optimization problems. Numerical Algorithms.
Crossref
Kaixin Gao, Zheng-Hai Huang & Lulu Guo. (2024) Low-rank matrix recovery problem minimizing a new ratio of two norms approximating the rank function then using an ADMM-type solver with applications. Journal of Computational and Applied Mathematics 438, pages 115564.
Crossref
Peng-Jie Liu, Jin-Bao Jian, Hu Shao, Xiao-Quan Wang, Jia-Wei Xu & Xiao-Yu Wu. (2024) A Bregman-Style Improved ADMM and its Linearized Version in the Nonconvex Setting: Convergence and Rate Analyses. Journal of the Operations Research Society of China.
Crossref
Zhongming Wu, Guoyu Xie, Zhili Ge & Valentina De Simone. (2023) Nonconvex multi-period mean-variance portfolio optimization. Annals of Operations Research 332:1-3, pages 617-644.
Crossref
Chicago Park, Shirin Shoushtari, Weijie Gan & Ulugbek S. Kamilov. (2023) Convergence of Nonconvex PNP-ADMM with MMSE Denoisers. Convergence of Nonconvex PNP-ADMM with MMSE Denoisers.
Miantao Chao, Yueqi Geng & Yongxin Zhao. (2023) A Method of Inertial Regularized ADMM for Separable Nonconvex Optimization Problems. Soft Computing 27:22, pages 16741-16757.
Crossref
Hengmin Zhang, Feng Qian, Peng Shi, Wenli Du, Yang Tang, Jianjun Qian, Chen Gong & Jian Yang. (2023) Generalized Nonconvex Nonsmooth Low-Rank Matrix Recovery Framework With Feasible Algorithm Designs and Convergence Analysis. IEEE Transactions on Neural Networks and Learning Systems 34:9, pages 5342-5353.
Crossref
Javier Salazar Cavazos, Jeffrey A. Fessler & Laura Balzano. (2023) ALPCAH: Sample-wise Heteroscedastic PCA with Tail Singular Value Regularization. ALPCAH: Sample-wise Heteroscedastic PCA with Tail Singular Value Regularization.
Qingsong Wang & Deren Han. (2023) A generalized inertial proximal alternating linearized minimization method for nonconvex nonsmooth problems. Applied Numerical Mathematics 189, pages 66-87.
Crossref
Shuang Liu, Yajun Wang, Zhuxian Lian, Yinjie Su & Zhibin Xie. (2023) Joint Suppression of PAPR and OOB Radiation for OFDM Systems. IEEE Transactions on Broadcasting 69:2, pages 528-537.
Crossref
Qingsong Wang, Zehui Liu, Chunfeng Cui & Deren Han. (2023) Inertial accelerated SGD algorithms for solving large-scale lower-rank tensor CP decomposition problems. Journal of Computational and Applied Mathematics 423, pages 114948.
Crossref
Xiaoquan Wang, Hu Shao, Pengjie Liu & Ting Wu. (2023) An inertial proximal partially symmetric ADMM-based algorithm for linearly constrained multi-block nonconvex optimization problems with applications. Journal of Computational and Applied Mathematics 420, pages 114821.
Crossref
Kaizhao Sun & X. Andy Sun. (2022) A two-level distributed algorithm for nonconvex constrained optimization. Computational Optimization and Applications 84:2, pages 609-649.
Crossref
Lei Hua, Yajun Wang, Zhuxian Lian, Yinjie Su & Zhibin Xie. (2023) LADMM-Based PAPR-Aware Precoding for Massive MIMO-OFDM Downlink Systems. IEEE Transactions on Vehicular Technology 72:1, pages 735-746.
Crossref
Zekun Liu & Siwei Yu. (2023) Alternating Direction Method of Multipliers Based on $\ell_{2,0}$-Norm for Multiple Measurement Vector Problem. IEEE Transactions on Signal Processing 71, pages 3490-3501.
Crossref
Mei Zhang, Zhiguo Wang, Feng Yin & Xiaojing Shen. (2023) Distributed Scaled Proximal ADMM Algorithms for Cooperative Localization in WSNs. IEEE Transactions on Signal Processing 71, pages 3312-3327.
Crossref
Xinyi Zuo & Yi Jiang. (2022) Solution methodologies for minimizing a sum of pointwise minima of two functions. Optimization Letters 17:1, pages 75-87.
Crossref
İlkay Yıldız, Jennifer Dy, Deniz Erdoğmuş, Susan Ostmo, J. Peter Campbell, Michael F. Chiang & Stratis Ioannidis. (2022) Spectral Ranking Regression. ACM Transactions on Knowledge Discovery from Data 16:6, pages 1-38.
Crossref
Jian Jinbao, Zhang Chen & Yin Jianghua. (2022) A Peaceman-Rachford splitting sequential quadratic programming method with double step-lengths for two-block nonconvex optimization. SCIENTIA SINICA Mathematica 52:12, pages 1449.
Crossref
Maryam Yashtini. (2022) Convergence and rate analysis of a proximal linearized ADMM for nonconvex nonsmooth optimization. Journal of Global Optimization 84:4, pages 913-939.
Crossref
Teng-Hui Huang, Aly El Gamal & Hesham El Gamal. (2022) On The Multi-View Information Bottleneck Representation. On The Multi-View Information Bottleneck Representation.
Xueying Zhao, Minru Bai, Defeng Sun & Libin Zheng. (2022) Robust Tensor Completion: Equivalent Surrogates, Error Bounds, and Algorithms. SIAM Journal on Imaging Sciences 15:2, pages 625-669.
Crossref
Jiawei Xu & Miantao Chao. (2021) An inertial Bregman generalized alternating direction method of multipliers for nonconvex optimization. Journal of Applied Mathematics and Computing 68:3, pages 1-27.
Crossref
Andreas Themelis, Lorenzo Stella & Panagiotis Patrinos. (2022) Douglas–Rachford splitting and ADMM for nonconvex optimization: accelerated and Newton-type linesearch algorithms. Computational Optimization and Applications 82:2, pages 395-440.
Crossref
Jingyan Xu & Frédéric Noo. (2022) Convex optimization algorithms in medical image reconstruction—in the age of AI. Physics in Medicine & Biology 67:7, pages 07TR01.
Crossref
Min Tao. (2022) Minimization of $L_1$ Over $L_2$ for Sparse Signal Recovery with Convergence Guarantee. SIAM Journal on Scientific Computing 44:2, pages A770-A797.
Crossref
Jun Zhang, Pengcheng Li, Junci Yang, Mingxi Ma & Chengzhi Deng. (2022) Poisson image restoration using a novel directional regularization . Signal Processing 193, pages 108407.
Crossref
Mingming Yin, Tarmizi Adam, Raveendran Paramesran & Mohd Fikree Hassan. (2022) An -overlapping group sparse total variation for impulse noise image restoration . Signal Processing: Image Communication 102, pages 116620.
Crossref
De-Ren Han. (2022) A Survey on Some Recent Developments of Alternating Direction Method of Multipliers. Journal of the Operations Research Society of China 10:1, pages 1-52.
Crossref
Chun Zhang, Yongzhong Song, Xingju Cai & Deren Han. (2021) An extended proximal ADMM algorithm for three-block nonconvex optimization problems. Journal of Computational and Applied Mathematics 398, pages 113681.
Crossref
Tingting Wu, Michael K. Ng & Xi-Le Zhao. (2021) Sparsity reconstruction using nonconvex TGpV-shearlet regularization and constrained projection. Applied Mathematics and Computation 410, pages 126170.
Crossref
Maksim V. Dolgopolik. (2021) The alternating direction method of multipliers for finding the distance between ellipsoids. Applied Mathematics and Computation 409, pages 126387.
Crossref
Maryam Yashtini. (2021) Multi-block Nonconvex Nonsmooth Proximal ADMM: Convergence and Rates Under Kurdyka–Łojasiewicz Property. Journal of Optimization Theory and Applications 190:3, pages 966-998.
Crossref
Zehui Jia, Jieru Huang & Zhongming Wu. (2021) An incremental aggregated proximal ADMM for linearly constrained nonconvex optimization with application to sparse logistic regression problems. Journal of Computational and Applied Mathematics 390, pages 113384.
Crossref
Tingting Wu, Xiaoyu Gu, Jinbo Shao, Ruoxuan Zhou & Zhi Li. (2021) Colour image segmentation based on a convex K‐means approach. IET Image Processing 15:8, pages 1596-1606.
Crossref
Jun-Feng Yang & Yin Zhang. (2019) Local Linear Convergence of an ADMM-Type Splitting Framework for Equality Constrained Optimization. Journal of the Operations Research Society of China 9:2, pages 307-319.
Crossref
Jingjing Liu, Ruijie Ma, Xiaoyang Zeng, Wanquan Liu, Mingyu Wang & Hui Chen. (2021) An efficient non-convex total variation approach for image deblurring and denoising. Applied Mathematics and Computation 397, pages 125977.
Crossref
Jiaqi Sun, Wenrui Dai, Chenglin Li, Junni Zou & Hongkai Xiong. (2021) Compressive Sensing via Unfolded $\ell_{0}$ -constrained Convolutional Sparse Coding. Compressive Sensing via Unfolded $\ell_{0}$ -constrained Convolutional Sparse Coding.
Chao Wang, Min Tao, James G. Nagy & Yifei Lou. (2021) Limited-Angle CT Reconstruction via the $L_1/L_2$ Minimization. SIAM Journal on Imaging Sciences 14:2, pages 749-777.
Crossref
Zehui Jia, Xue Gao, Xingju Cai & Deren Han. (2021) Local Linear Convergence of the Alternating Direction Method of Multipliers for Nonconvex Separable Optimization Problems. Journal of Optimization Theory and Applications 188:1, pages 1-25.
Crossref
Sean Holman & Philip Richardson. (2020) SPECT with a multi-bang assumption on attenuation. Inverse Problems 36:12, pages 125005.
Crossref
Radu Ioan Boţ & Dang-Khoa Nguyen. (2020) The Proximal Alternating Direction Method of Multipliers in the Nonconvex Setting: Convergence Analysis and Rates. Mathematics of Operations Research 45:2, pages 682-712.
Crossref
Kai Tu, Haibin Zhang, Huan Gao & Junkai Feng. (2019) A hybrid Bregman alternating direction method of multipliers for the linearly constrained difference-of-convex problems. Journal of Global Optimization 76:4, pages 665-693.
Crossref
Miantao Chao, Zhao Deng & Jinbao Jian. (2020) Convergence of Linear Bregman ADMM for Nonconvex and Nonsmooth Problems with Nonseparable Structure. Complexity 2020, pages 1-14.
Crossref
Zhi-Feng Pang, Hui-Li Zhang, Shousheng Luo & Tieyong Zeng. (2020) Image denoising based on the adaptive weighted TV regularization. Signal Processing 167, pages 107325.
Crossref
惠晴 胡. (2020) Regualized Alternating Direction Method of Multiplies for Nonseparable Nonconvex Problem. Pure Mathematics 10:07, pages 655-665.
Crossref
Andreas Themelis & Panagiotis Patrinos. (2020) Douglas--Rachford Splitting and ADMM for Nonconvex Optimization: Tight Convergence Results. SIAM Journal on Optimization 30:1, pages 149-181.
Crossref
Chun Zhang, Yanhong Yang, Zeyan Wang & Yongxin Chen. (2020) A Linearized Alternating Direction Method of Multipliers for a Special Three-Block Nonconvex Optimization Problem of Background/Foreground Extraction. IEEE Access 8, pages 198886-198899.
Crossref
Min Li & Zhongming Wu. (2019) Convergence Analysis of the Generalized Splitting Methods for a Class of Nonconvex Optimization Problems. Journal of Optimization Theory and Applications 183:2, pages 535-565.
Crossref
Xianchao Xiu, Wanquan Liu, Ling Li & Lingchen Kong. (2019) Alternating direction method of multipliers for nonconvex fused regression problems. Computational Statistics & Data Analysis 136, pages 59-71.
Crossref
Kun Shang, Yu-Fan Li & Zheng-Hai Huang. (2019) Iterative p-shrinkage thresholding algorithm for low Tucker rank tensor recovery. Information Sciences 482, pages 374-391.
Crossref
Yaghoub Rahimi, Chao Wang, Hongbo Dong & Yifei Lou. (2019) A Scale-Invariant Approach for Sparse Signal Recovery. SIAM Journal on Scientific Computing 41:6, pages A3649-A3672.
Crossref
Qinghua Liu, Xinyue Shen & Yuantao Gu. (2019) Linearized ADMM for Nonconvex Nonsmooth Optimization With Convergence Analysis. IEEE Access 7, pages 76131-76144.
Crossref
Jiabin Zheng, Mingbo Liu, Wentian Lu, Min Xie & Jianquan Zhu. (2018) Extended ADMMs for RPO of large‐scale power systems with discrete controls. IET Generation, Transmission & Distribution 12:11, pages 2624-2632.
Crossref
Yu-Fan Li, Kun Shang & Zheng-Hai Huang. (2018) Low Tucker rank tensor recovery via ADMM based on exact and inexact iteratively reweighted algorithms. Journal of Computational and Applied Mathematics 331, pages 64-81.
Crossref
Jong-Shi Pang & Min Tao. (2018) Decomposition Methods for Computing Directional Stationary Solutions of a Class of Nonsmooth Nonconvex Optimization Problems. SIAM Journal on Optimization 28:2, pages 1640-1669.
Crossref
Zhongming Wu, Min Li, David Z. W. Wang & Deren Han. (2017) A Symmetric Alternating Direction Method of Multipliers for Separable Nonconvex Minimization Problems. Asia-Pacific Journal of Operational Research 34:06, pages 1750030.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.