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Componentwise versus global approaches to nonsmooth multiobjective optimization
On the absence of duality gap for Lagrange-type functions
1. | Engenharia de Sistemas e Computacao/COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil |
2. | School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, Australia |
[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] |
Jen-Yen Lin, Hui-Ju Chen, Ruey-Lin Sheu. Augmented Lagrange primal-dual approach for generalized fractional programming problems. Journal of Industrial and Management Optimization, 2013, 9 (4) : 723-741. doi: 10.3934/jimo.2013.9.723 |
[3] |
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 |
[4] |
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 |
[5] |
Tengteng Yu, Xin-Wei Liu, Yu-Hong Dai, Jie Sun. Variable metric proximal stochastic variance reduced gradient methods for nonconvex nonsmooth optimization. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021084 |
[6] |
Aleksandar Jović. Saddle-point type optimality criteria, duality and a new approach for solving nonsmooth fractional continuous-time programming problems. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022025 |
[7] |
Mohamed Aly Tawhid. Nonsmooth generalized complementarity as unconstrained optimization. Journal of Industrial and Management Optimization, 2010, 6 (2) : 411-423. doi: 10.3934/jimo.2010.6.411 |
[8] |
Qian Liu, Xinmin Yang, Heung Wing Joseph Lee. On saddle points of a class of augmented lagrangian functions. Journal of Industrial and Management Optimization, 2007, 3 (4) : 693-700. doi: 10.3934/jimo.2007.3.693 |
[9] |
Caiping Liu, Heungwing Lee. Lagrange multiplier rules for approximate solutions in vector optimization. Journal of Industrial and Management Optimization, 2012, 8 (3) : 749-764. doi: 10.3934/jimo.2012.8.749 |
[10] |
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 |
[11] |
Giancarlo Bigi. Componentwise versus global approaches to nonsmooth multiobjective optimization. Journal of Industrial and Management Optimization, 2005, 1 (1) : 21-32. doi: 10.3934/jimo.2005.1.21 |
[12] |
Nobuko Sagara, Masao Fukushima. trust region method for nonsmooth convex optimization. Journal of Industrial and Management Optimization, 2005, 1 (2) : 171-180. doi: 10.3934/jimo.2005.1.171 |
[13] |
Ye Tian, Cheng Lu. Nonconvex quadratic reformulations and solvable conditions for mixed integer quadratic programming problems. Journal of Industrial and Management Optimization, 2011, 7 (4) : 1027-1039. doi: 10.3934/jimo.2011.7.1027 |
[14] |
Dan Xue, Wenyu Sun, Hongjin He. A structured trust region method for nonconvex programming with separable structure. Numerical Algebra, Control and Optimization, 2013, 3 (2) : 283-293. doi: 10.3934/naco.2013.3.283 |
[15] |
Xian-Jun Long, Jing Quan. Optimality conditions and duality for minimax fractional programming involving nonsmooth generalized univexity. Numerical Algebra, Control and Optimization, 2011, 1 (3) : 361-370. doi: 10.3934/naco.2011.1.361 |
[16] |
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 |
[17] |
Najeeb Abdulaleem. Optimality and duality for $ E $-differentiable multiobjective programming problems involving $ E $-type Ⅰ functions. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022004 |
[18] |
Yuying Zhou, Gang Li. The Toland-Fenchel-Lagrange duality of DC programs for composite convex functions. Numerical Algebra, Control and Optimization, 2014, 4 (1) : 9-23. doi: 10.3934/naco.2014.4.9 |
[19] |
Gonglin Yuan, Zhan Wang, Pengyuan Li. Global convergence of a modified Broyden family method for nonconvex functions. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021164 |
[20] |
Zehui Jia, Xue Gao, Xingju Cai, Deren Han. The convergence rate analysis of the symmetric ADMM for the nonconvex separable optimization problems. Journal of Industrial and Management Optimization, 2021, 17 (4) : 1943-1971. doi: 10.3934/jimo.2020053 |
2020 Impact Factor: 1.801
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