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On saddle points of a class of augmented lagrangian functions
| 1. | Department of Mathematics, Inner Mongolia University, Hohhot, 010021, China |
| 2. | Department of Mathematics, Chongqing Normal University, Chongqing 400047 |
| 3. | Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China |
| [1] |
Chunrong Chen, T. C. Edwin Cheng, Shengji Li, Xiaoqi Yang. Nonlinear augmented Lagrangian for nonconvex multiobjective optimization. Journal of Industrial and Management Optimization, 2011, 7 (1) : 157-174. doi: 10.3934/jimo.2011.7.157 |
| [2] |
Chunrong Chen. A unified nonlinear augmented Lagrangian approach for nonconvex vector optimization. Numerical Algebra, Control and Optimization, 2011, 1 (3) : 495-508. doi: 10.3934/naco.2011.1.495 |
| [3] |
Yuan Shen, Wenxing Zhang, Bingsheng He. Relaxed augmented Lagrangian-based proximal point algorithms for convex optimization with linear constraints. Journal of Industrial and Management Optimization, 2014, 10 (3) : 743-759. doi: 10.3934/jimo.2014.10.743 |
| [4] |
Xueyong Wang, Yiju Wang, Gang Wang. An accelerated augmented Lagrangian method for multi-criteria optimization problem. Journal of Industrial and Management Optimization, 2020, 16 (1) : 1-9. doi: 10.3934/jimo.2018136 |
| [5] |
Qingsong Duan, Mengwei Xu, Yue Lu, Liwei Zhang. A smoothing augmented Lagrangian method for nonconvex, nonsmooth constrained programs and its applications to bilevel problems. Journal of Industrial and Management Optimization, 2019, 15 (3) : 1241-1261. doi: 10.3934/jimo.2018094 |
| [6] |
Liping Tang, Ying Gao. Some properties of nonconvex oriented distance function and applications to vector optimization problems. Journal of Industrial and Management Optimization, 2021, 17 (1) : 485-500. doi: 10.3934/jimo.2020117 |
| [7] |
Yang Li, Liwei Zhang. A nonlinear Lagrangian method based on Log-Sigmoid function for nonconvex semidefinite programming. Journal of Industrial and Management Optimization, 2009, 5 (3) : 651-669. doi: 10.3934/jimo.2009.5.651 |
| [8] |
Behrouz Kheirfam. A full Nesterov-Todd step infeasible interior-point algorithm for symmetric optimization based on a specific kernel function. Numerical Algebra, Control and Optimization, 2013, 3 (4) : 601-614. doi: 10.3934/naco.2013.3.601 |
| [9] |
Siqi Li, Weiyi Qian. Analysis of complexity of primal-dual interior-point algorithms based on a new kernel function for linear optimization. Numerical Algebra, Control and Optimization, 2015, 5 (1) : 37-46. doi: 10.3934/naco.2015.5.37 |
| [10] |
Ayache Benhadid, Fateh Merahi. Complexity analysis of an interior-point algorithm for linear optimization based on a new parametric kernel function with a double barrier term. Numerical Algebra, Control and Optimization, 2022 doi: 10.3934/naco.2022003 |
| [11] |
Li Jin, Hongying Huang. Differential equation method based on approximate augmented Lagrangian for nonlinear programming. Journal of Industrial and Management Optimization, 2020, 16 (5) : 2267-2281. doi: 10.3934/jimo.2019053 |
| [12] |
Chunlin Wu, Juyong Zhang, Xue-Cheng Tai. Augmented Lagrangian method for total variation restoration with non-quadratic fidelity. Inverse Problems and Imaging, 2011, 5 (1) : 237-261. doi: 10.3934/ipi.2011.5.237 |
| [13] |
Wei Zhu, Xue-Cheng Tai, Tony Chan. Augmented Lagrangian method for a mean curvature based image denoising model. Inverse Problems and Imaging, 2013, 7 (4) : 1409-1432. doi: 10.3934/ipi.2013.7.1409 |
| [14] |
Fatemeh Bazikar, Saeed Ketabchi, Hossein Moosaei. Smooth augmented Lagrangian method for twin bounded support vector machine. Numerical Algebra, Control and Optimization, 2021 doi: 10.3934/naco.2021027 |
| [15] |
Guoqiang Wang, Zhongchen Wu, Zhongtuan Zheng, Xinzhong Cai. Complexity analysis of primal-dual interior-point methods for semidefinite optimization based on a parametric kernel function with a trigonometric barrier term. Numerical Algebra, Control and Optimization, 2015, 5 (2) : 101-113. doi: 10.3934/naco.2015.5.101 |
| [16] |
Ovide Arino, Eva Sánchez. A saddle point theorem for functional state-dependent delay differential equations. Discrete and Continuous Dynamical Systems, 2005, 12 (4) : 687-722. doi: 10.3934/dcds.2005.12.687 |
| [17] |
Xiao-Fei Peng, Wen Li. A new Bramble-Pasciak-like preconditioner for saddle point problems. Numerical Algebra, Control and Optimization, 2012, 2 (4) : 823-838. doi: 10.3934/naco.2012.2.823 |
| [18] |
Xi-Hong Yan. A new convergence proof of augmented Lagrangian-based method with full Jacobian decomposition for structured variational inequalities. Numerical Algebra, Control and Optimization, 2016, 6 (1) : 45-54. doi: 10.3934/naco.2016.6.45 |
| [19] |
Anis Theljani, Ke Chen. An augmented lagrangian method for solving a new variational model based on gradients similarity measures and high order regulariation for multimodality registration. Inverse Problems and Imaging, 2019, 13 (2) : 309-335. doi: 10.3934/ipi.2019016 |
| [20] |
Wei Zhu. A numerical study of a mean curvature denoising model using a novel augmented Lagrangian method. Inverse Problems and Imaging, 2017, 11 (6) : 975-996. doi: 10.3934/ipi.2017045 |
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