-
Previous Article
Advance selling decisions with overconfident consumers
- JIMO Home
- This Issue
-
Next Article
Equilibrium balking strategies in renewal input queue with Bernoulli-schedule controlled vacation and vacation interruption
An augmented Lagrangian-based parallel splitting method for a one-leader-two-follower game
1. | Department of Mathematics, Taiyuan Normal University, Taiyuan 030012, Shanxi Province, China |
References:
[1] |
G. Chen and M. Teboulle, A proximal-based decomposition method for convex minimization problems, Mathematical Programming, 64 (1994), 81-101.
doi: 10.1007/BF01582566. |
[2] |
J. Eckstein and D. P. Bertsekas, On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, 55 (1992), 293-318.
doi: 10.1007/BF01581204. |
[3] |
M. Fukushima, Application of the alternating direction method of multipliers to separable convex programming problems, Computational Optimization and Applications, 1 (1992), 93-111.
doi: 10.1007/BF00247655. |
[4] |
D. Gabay and B. Mercier, A dual algorithm for the solution of nonlinear variational problems via finite element approximations, Computers and Mathematics with Applications, 2 (1976), 17-40.
doi: 10.1016/0898-1221(76)90003-1. |
[5] |
R. Glowinski and P. Le Tallec, Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics, SIAM Studies in Applied Mathematics, SIAM, Philadelphia, 1989.
doi: 10.1137/1.9781611970838. |
[6] |
D. Han, H. He, H. Yang and X. Yuan, A customized Douglas-Rachford splitting algorithm for separable convex minimization with linear constraints, Numerische Mathematik, 127 (2014), 167-200.
doi: 10.1007/s00211-013-0580-2. |
[7] |
B. S. He, Inexact implicit methods for monotone general variational inequalities, Mathematical Programming, 86 (1999), 199-217.
doi: 10.1007/s101070050086. |
[8] |
B. S. He, Parallel splitting augmented Lagrangian methods for monotone structured variational inequalities, Computational Optimization and Applications, 42 (2009), 195-212.
doi: 10.1007/s10589-007-9109-x. |
[9] |
B. S. He, L. Z. Liao, D. Han and H. Yang, A new inexact alternating directions method for monotone variational inequalities, Mathematical Programming 92 (2002), 103-118.
doi: 10.1007/s101070100280. |
[10] |
B. S. He, Y. Xu and X. M. Yuan, A logarithmic-quadratic proximal prediction-correction method for structured monotone variational inequalities, Computational Optimization and Applications, 35 (2006), 19-46.
doi: 10.1007/s10589-006-6442-4. |
[11] |
S. Kontogiorgis and R. Meyer, A variable-penalty alternating directions method for convex optimization, Mathematical Programming, 83 (1998), 29-53.
doi: 10.1007/BF02680549. |
[12] |
A. Nagurney and D. Zhang, Projected Dynamical Systems and Variational Inequalities with Applications, Kluwer, Boston, 1996.
doi: 10.1007/978-1-4615-2301-7. |
[13] |
M. Tao and X. Yuan, An inexact parallel splitting augmented Lagrangian method for monotone variational inequalities with separable structures, Computational Optimization and Applications, 52 (2012), 439-461.
doi: 10.1007/s10589-011-9417-z. |
[14] |
P. Tseng, Alternating projection-proximal methods for convex programming and variational inequalities, SIAM Journal on Optimization, 7 (1997), 951-965.
doi: 10.1137/S1052623495279797. |
[15] |
K. Wang, L. Xu and D. Han, A new parallel splitting descent method for structured variational inequalities, Journal of Industrial and Management Optimization, 10 (2014), 461-476.
doi: 10.3934/jimo.2014.10.461. |
show all references
References:
[1] |
G. Chen and M. Teboulle, A proximal-based decomposition method for convex minimization problems, Mathematical Programming, 64 (1994), 81-101.
doi: 10.1007/BF01582566. |
[2] |
J. Eckstein and D. P. Bertsekas, On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, 55 (1992), 293-318.
doi: 10.1007/BF01581204. |
[3] |
M. Fukushima, Application of the alternating direction method of multipliers to separable convex programming problems, Computational Optimization and Applications, 1 (1992), 93-111.
doi: 10.1007/BF00247655. |
[4] |
D. Gabay and B. Mercier, A dual algorithm for the solution of nonlinear variational problems via finite element approximations, Computers and Mathematics with Applications, 2 (1976), 17-40.
doi: 10.1016/0898-1221(76)90003-1. |
[5] |
R. Glowinski and P. Le Tallec, Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics, SIAM Studies in Applied Mathematics, SIAM, Philadelphia, 1989.
doi: 10.1137/1.9781611970838. |
[6] |
D. Han, H. He, H. Yang and X. Yuan, A customized Douglas-Rachford splitting algorithm for separable convex minimization with linear constraints, Numerische Mathematik, 127 (2014), 167-200.
doi: 10.1007/s00211-013-0580-2. |
[7] |
B. S. He, Inexact implicit methods for monotone general variational inequalities, Mathematical Programming, 86 (1999), 199-217.
doi: 10.1007/s101070050086. |
[8] |
B. S. He, Parallel splitting augmented Lagrangian methods for monotone structured variational inequalities, Computational Optimization and Applications, 42 (2009), 195-212.
doi: 10.1007/s10589-007-9109-x. |
[9] |
B. S. He, L. Z. Liao, D. Han and H. Yang, A new inexact alternating directions method for monotone variational inequalities, Mathematical Programming 92 (2002), 103-118.
doi: 10.1007/s101070100280. |
[10] |
B. S. He, Y. Xu and X. M. Yuan, A logarithmic-quadratic proximal prediction-correction method for structured monotone variational inequalities, Computational Optimization and Applications, 35 (2006), 19-46.
doi: 10.1007/s10589-006-6442-4. |
[11] |
S. Kontogiorgis and R. Meyer, A variable-penalty alternating directions method for convex optimization, Mathematical Programming, 83 (1998), 29-53.
doi: 10.1007/BF02680549. |
[12] |
A. Nagurney and D. Zhang, Projected Dynamical Systems and Variational Inequalities with Applications, Kluwer, Boston, 1996.
doi: 10.1007/978-1-4615-2301-7. |
[13] |
M. Tao and X. Yuan, An inexact parallel splitting augmented Lagrangian method for monotone variational inequalities with separable structures, Computational Optimization and Applications, 52 (2012), 439-461.
doi: 10.1007/s10589-011-9417-z. |
[14] |
P. Tseng, Alternating projection-proximal methods for convex programming and variational inequalities, SIAM Journal on Optimization, 7 (1997), 951-965.
doi: 10.1137/S1052623495279797. |
[15] |
K. Wang, L. Xu and D. Han, A new parallel splitting descent method for structured variational inequalities, Journal of Industrial and Management Optimization, 10 (2014), 461-476.
doi: 10.3934/jimo.2014.10.461. |
[1] |
Xin Yang, Nan Wang, Lingling Xu. A parallel Gauss-Seidel method for convex problems with separable structure. Numerical Algebra, Control and Optimization, 2020, 10 (4) : 557-570. doi: 10.3934/naco.2020051 |
[2] |
Kai Wang, Lingling Xu, Deren Han. A new parallel splitting descent method for structured variational inequalities. Journal of Industrial and Management Optimization, 2014, 10 (2) : 461-476. doi: 10.3934/jimo.2014.10.461 |
[3] |
Zhili Ge, Gang Qian, Deren Han. Global convergence of an inexact operator splitting method for monotone variational inequalities. Journal of Industrial and Management Optimization, 2011, 7 (4) : 1013-1026. doi: 10.3934/jimo.2011.7.1013 |
[4] |
Sara Bernardi, Gissell Estrada-Rodriguez, Heiko Gimperlein, Kevin J. Painter. Macroscopic descriptions of follower-leader systems. Kinetic and Related Models, 2021, 14 (6) : 981-1002. doi: 10.3934/krm.2021035 |
[5] |
Yekini Shehu, Olaniyi Iyiola. On a modified extragradient method for variational inequality problem with application to industrial electricity production. Journal of Industrial and Management Optimization, 2019, 15 (1) : 319-342. doi: 10.3934/jimo.2018045 |
[6] |
Yarui Duan, Pengcheng Wu, Yuying Zhou. Penalty approximation method for a double obstacle quasilinear parabolic variational inequality problem. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022017 |
[7] |
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 |
[8] |
Su-Hong Jiang, Min Li. A modified strictly contractive peaceman-rachford splitting method for multi-block separable convex programming. Journal of Industrial and Management Optimization, 2018, 14 (1) : 397-412. doi: 10.3934/jimo.2017052 |
[9] |
Changjun Yu, Kok Lay Teo, Liansheng Zhang, Yanqin Bai. On a refinement of the convergence analysis for the new exact penalty function method for continuous inequality constrained optimization problem. Journal of Industrial and Management Optimization, 2012, 8 (2) : 485-491. doi: 10.3934/jimo.2012.8.485 |
[10] |
Francis Akutsah, Akindele Adebayo Mebawondu, Hammed Anuoluwapo Abass, Ojen Kumar Narain. A self adaptive method for solving a class of bilevel variational inequalities with split variational inequality and composed fixed point problem constraints in Hilbert spaces. Numerical Algebra, Control and Optimization, 2021 doi: 10.3934/naco.2021046 |
[11] |
S. J. Li, Z. M. Fang. On the stability of a dual weak vector variational inequality problem. Journal of Industrial and Management Optimization, 2008, 4 (1) : 155-165. doi: 10.3934/jimo.2008.4.155 |
[12] |
Yoshifumi Aimoto, Takayasu Matsuo, Yuto Miyatake. A local discontinuous Galerkin method based on variational structure. Discrete and Continuous Dynamical Systems - S, 2015, 8 (5) : 817-832. doi: 10.3934/dcdss.2015.8.817 |
[13] |
Li Wang, Yang Li, Liwei Zhang. A differential equation method for solving box constrained variational inequality problems. Journal of Industrial and Management Optimization, 2011, 7 (1) : 183-198. doi: 10.3934/jimo.2011.7.183 |
[14] |
Hui-Qiang Ma, Nan-Jing Huang. Neural network smoothing approximation method for stochastic variational inequality problems. Journal of Industrial and Management Optimization, 2015, 11 (2) : 645-660. doi: 10.3934/jimo.2015.11.645 |
[15] |
Ming Chen, Chongchao Huang. A power penalty method for a class of linearly constrained variational inequality. Journal of Industrial and Management Optimization, 2018, 14 (4) : 1381-1396. doi: 10.3934/jimo.2018012 |
[16] |
Walter Allegretto, Yanping Lin, Shuqing Ma. On the box method for a non-local parabolic variational inequality. Discrete and Continuous Dynamical Systems - B, 2001, 1 (1) : 71-88. doi: 10.3934/dcdsb.2001.1.71 |
[17] |
Shuang Chen, Li-Ping Pang, Dan Li. An inexact semismooth Newton method for variational inequality with symmetric cone constraints. Journal of Industrial and Management Optimization, 2015, 11 (3) : 733-746. doi: 10.3934/jimo.2015.11.733 |
[18] |
Chibueze Christian Okeke, Abdulmalik Usman Bello, Lateef Olakunle Jolaoso, Kingsley Chimuanya Ukandu. Inertial method for split null point problems with pseudomonotone variational inequality problems. Numerical Algebra, Control and Optimization, 2021 doi: 10.3934/naco.2021037 |
[19] |
Yaonan Ma, Li-Zhi Liao. The Glowinski–Le Tallec splitting method revisited: A general convergence and convergence rate analysis. Journal of Industrial and Management Optimization, 2021, 17 (4) : 1681-1711. doi: 10.3934/jimo.2020040 |
[20] |
T. A. Shaposhnikova, M. N. Zubova. Homogenization problem for a parabolic variational inequality with constraints on subsets situated on the boundary of the domain. Networks and Heterogeneous Media, 2008, 3 (3) : 675-689. doi: 10.3934/nhm.2008.3.675 |
2021 Impact Factor: 1.411
Tools
Metrics
Other articles
by authors
[Back to Top]