[1] Donoho D L. High-dimensional Data Analysis: The Curses and Blessings of Dimensionality[M]. AMS Math Challenges Lecture, 2000.
[2] Boyd S, Parikh N, Chu E, et al. Distributed optimization and statistical learning via the alternating direction method of multipliers[J]. Foundations and Trends in Machine learning, 2011, 3(1): 1–122.
[3] Han D R. A survey on some recent developments of alternating direction method of multipliers[J]. Journal of the Operations Research Society of China, 2022, 10(1): 1–52.
[4] Gabay D. Chapter IX Applications of the Method of Multipliers to Variational Inequalities[M]. Studies in mathematics and its applications. Elsevier, 1983, 15: 299–331.
[5] He B, Liu H, Wang Z, et al. A strictly contractive Peaceman-Rachford splitting method for convex programming[J]. SIAM Journal on Optimization, 2014, 24(3): 1011–1040.
[6] Li X X, Yuan X M. A proximal strictly contractive Peaceman-Rachford splitting method for convex programming with application to imaging[J]. SIAM Journal on Imaging Sciences, 2015, 8: 1332–1365.
[7] Li M, Yuan X M. A strictly contractive Peaceman-Rachford splitting method with logarithmicquadratic proximal regularization for convex programming[J]. Mathematics of Operations Research, 2015, 40: 842–858.
[8] He B, Ma F, Yuan X. Convergence study on the symmetric version of ADMM with larger step sizes[J]. SIAM Journal on Imaging Sciences, 2016, 9(3): 1467–1501.
[9] Chen Y N, Dai Y H, Han D R. Fiber orientation distribution estimation using a PeacemanRachford splitting method[J]. SIAM Journal on Imaging Sciences, 2016, 9: 573–604.
[10] Hong M, Luo Z Q, Razaviyayn M. Convergence analysis of alternating direction method of multipliers for a family of nonconvex problems[J]. SIAM Journal on Optimization, 2016, 26(1): 337–364.
[11] Cui Y, Li X, Sun D, et al. On the convergence properties of a majorized alternating direction method of multipliers for linearly constrained convex optimization problems with coupled objective functions[J]. Journal of Optimization Theory and Applications, 2016, 169(3): 1013–1041.
[12] Gao X, Zhang S Z. First-order algorithms for convex optimization with nonseparable objective and coupled constraints[J]. Journal of the Operations Research Society of China, 2017, 5(2): 131–159.
[13] Chen C, Li M, Liu X, et al. Extended ADMM and BCD for nonseparable convex minimization models with quadratic coupling terms: Convergence analysis and insights[J]. Mathematical Programming, 2019, 173(1): 37–77.
[14] Li P, Shen Y, Jiang S, et al. Convergence study on strictly contractive Peaceman-Rachford s plitting method for nonseparable convex minimization models with quadratic coupling terms[J]. Computational Optimization and Applications, 2021, 78(1): 87–124.
[15] Nikolova M, Ng M K, Zhang S, et al. Efficient reconstruction of piecewise constant images using nonsmooth nonconvex minimization[J]. SIAM Journal on Imaging Sciences, 2008, 1(1): 2–25.
[16] Gu S H, Zhang L, Zuo W M, et al. Weighted nuclear norm minimization with application to image denoising[C]. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2014, 2862–2869.
[17] Bian W, Chen X. Linearly constrained non-Lipschitz optimization for image restoration[J]. SIAM Journal on Imaging Sciences, 2015, 8(4): 2294–2322.
[18] Liu J, Yuan L, Ye J. Dictionary lasso: Guaranteed sparse recovery under linear transformation[J]. arXiv preprint arXiv:1305.0047, 2013.
[19] Theerthamalai A, Maheswarapu S. An effective non-iterative “λ-logic based” algorithm for eco nomic dispatch of generators with cubic fuel cost function[J]. International Journal of Electrical Power and Energy Systems, 2010, 32(5): 539–542.
[20] Zhan J, Wu Q H, Guo C, et al. Economic dispatch with non-smooth objectives-part I: Local minimum analysis[J]. IEEE Transactions on Power Systems, 2014, 30(2): 710–721.
[21] 简金宝, 刘鹏杰, 江羡珍. 非凸多分块优化部分对称正则化交替方向乘子法[J]. 数学学报, 2021, 64(6): 1005–1026.
[22] Guo K, Han D, Wu T. Convergence of ADMM for optimization problems with nonseparable nonconvex objective and linear constraints[J]. Pacific Journal of Optimization, 2018, 14(3): 489–506.
[23] Guo K, Wang X. Convergence of generalized alternating direction method of multipliers for non separable nonconvex objective with linear constraints[J]. Journal of Mathematical Research with Applications, 2018, 38(5): 523–540.
[24] Chao M, Deng Z, Jian J. Convergence of linear Bregman ADMM for nonconvex and nonsmooth problems with nonseparable structure[J]. Complexity, 2020, 2020: 6237942.
[25] 刘鹏杰, 简金宝, 马国栋, 等. 非凸不可分优化线性近似Bregman型Peaceman-Rachford分裂算法[J]. 数学学报, 2023, 66(1): 75–94.
[26] Wang Y, Yin W, Zeng J. Global convergence of ADMM in nonconvex nonsmooth optimization[J]. Journal of Scientific Computing, 2019, 78(1): 29–63.
[27] Jiang B, Lin T, Ma S, et al. Structured nonconvex and nonsmooth optimization: Algorithms and iteration complexity analysis[J]. Computational Optimization and Applications, 2019, 72(1): 115–157.
[28] Hien L T K, Phan D N, Gillis N. A framework of inertial alternating direction method of multipliers for non-convex non-smooth optimization[J]. arXiv preprint arXiv:2102.05433, 2021.
[29] 简金宝, 劳译娴, 晁绵涛, 等. 线性约束两分块非凸优化的ADMM-SQP算法[J]. 运筹学学报, 2018, 22(2): 79–92.
[30] Jian J, Zhang C, Yin J, et al. Monotone splitting sequential quadratic optimization algorithm with applications in electric power systems[J]. Journal of Optimization Theory and Applications, 2020, 186(1): 226–247.
[31] 简金宝, 张晨, 尹江华. 两分块非凸优化\ Peaceman-Rachford\ 分裂序列二次规划双步长算法[J]. 中国科学: 数学, 2022. DOI: 10.1360/SSM-2020-0297
[32] Nesterov Y. Introductory Lectures on Convex Optimization: A Basic Course[M]. Springer Science & Business Media, 2003.
[33] 简金宝. 光滑约束优化快速算法: 理论分析与数值实验[M]. 北京: 科学出版社, 2010.
[34] Fukushima M. 著, 林贵华译. 非线性最优化基础[M]. 北京: 科学出版社, 2011.
[35] Rockafellar R T, Wets R J B. Variational Analysis[M]. Springer Science & Business Media, 2009.
[36] Li G, Pong T K. Global convergence of splitting methods for nonconvex composite optimization[J]. SIAM Journal on Optimization, 2015, 25(4): 2434–2460.
[37] Zeng L, Xie J. Group variable selection via SCAD-L2[J]. Statistics, 2014, 48(1): 49–66.
[38] Fan J. Comments on “wavelets in statistics: A review” by A. Antoniadis[J]. Journal of the Italian Statistical Society, 1997, 6(2): 131–138.
[39] Wu Z, Li M. General inertial proximal gradient method for a class of nonconvex nonsmooth optimization problems[J]. Computational Optimization and Applications, 2019, 73(1): 129–158.