-
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.
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.
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.
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.
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, (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.
doi: 10.1007/s00211-013-0580-2. |
[7] |
B. S. He, Inexact implicit methods for monotone general variational inequalities,, Mathematical Programming, 86 (1999), 199.
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.
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), 92 (2002), 103.
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.
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.
doi: 10.1007/BF02680549. |
[12] |
A. Nagurney and D. Zhang, Projected Dynamical Systems and Variational Inequalities with Applications,, Kluwer, (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.
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.
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.
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.
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.
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.
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.
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, (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.
doi: 10.1007/s00211-013-0580-2. |
[7] |
B. S. He, Inexact implicit methods for monotone general variational inequalities,, Mathematical Programming, 86 (1999), 199.
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.
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), 92 (2002), 103.
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.
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.
doi: 10.1007/BF02680549. |
[12] |
A. Nagurney and D. Zhang, Projected Dynamical Systems and Variational Inequalities with Applications,, Kluwer, (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.
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.
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.
doi: 10.3934/jimo.2014.10.461. |
[1] |
Armin Lechleiter, Tobias Rienmüller. Factorization method for the inverse Stokes problem. Inverse Problems & Imaging, 2013, 7 (4) : 1271-1293. doi: 10.3934/ipi.2013.7.1271 |
[2] |
Petra Csomós, Hermann Mena. Fourier-splitting method for solving hyperbolic LQR problems. Numerical Algebra, Control & Optimization, 2018, 8 (1) : 17-46. doi: 10.3934/naco.2018002 |
[3] |
Xiaomao Deng, Xiao-Chuan Cai, Jun Zou. A parallel space-time domain decomposition method for unsteady source inversion problems. Inverse Problems & Imaging, 2015, 9 (4) : 1069-1091. doi: 10.3934/ipi.2015.9.1069 |
[4] |
Manfred Einsiedler, Elon Lindenstrauss. On measures invariant under diagonalizable actions: the Rank-One case and the general Low-Entropy method. Journal of Modern Dynamics, 2008, 2 (1) : 83-128. doi: 10.3934/jmd.2008.2.83 |
[5] |
Marion Darbas, Jérémy Heleine, Stephanie Lohrengel. Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations. Inverse Problems & Imaging, 2020, 14 (6) : 1107-1133. doi: 10.3934/ipi.2020056 |
[6] |
David Cantala, Juan Sebastián Pereyra. Endogenous budget constraints in the assignment game. Journal of Dynamics & Games, 2015, 2 (3&4) : 207-225. doi: 10.3934/jdg.2015002 |
[7] |
V. Kumar Murty, Ying Zong. Splitting of abelian varieties. Advances in Mathematics of Communications, 2014, 8 (4) : 511-519. doi: 10.3934/amc.2014.8.511 |
[8] |
Sergi Simon. Linearised higher variational equations. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4827-4854. doi: 10.3934/dcds.2014.34.4827 |
[9] |
Xue-Ping Luo, Yi-Bin Xiao, Wei Li. Strict feasibility of variational inclusion problems in reflexive Banach spaces. Journal of Industrial & Management Optimization, 2020, 16 (5) : 2495-2502. doi: 10.3934/jimo.2019065 |
[10] |
Emma D'Aniello, Saber Elaydi. The structure of $ \omega $-limit sets of asymptotically non-autonomous discrete dynamical systems. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 903-915. doi: 10.3934/dcdsb.2019195 |
[11] |
Alexandr Mikhaylov, Victor Mikhaylov. Dynamic inverse problem for Jacobi matrices. Inverse Problems & Imaging, 2019, 13 (3) : 431-447. doi: 10.3934/ipi.2019021 |
[12] |
J. Frédéric Bonnans, Justina Gianatti, Francisco J. Silva. On the convergence of the Sakawa-Shindo algorithm in stochastic control. Mathematical Control & Related Fields, 2016, 6 (3) : 391-406. doi: 10.3934/mcrf.2016008 |
[13] |
Fernando P. da Costa, João T. Pinto, Rafael Sasportes. On the convergence to critical scaling profiles in submonolayer deposition models. Kinetic & Related Models, 2018, 11 (6) : 1359-1376. doi: 10.3934/krm.2018053 |
[14] |
Alberto Bressan, Carlotta Donadello. On the convergence of viscous approximations after shock interactions. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 29-48. doi: 10.3934/dcds.2009.23.29 |
[15] |
Caifang Wang, Tie Zhou. The order of convergence for Landweber Scheme with $\alpha,\beta$-rule. Inverse Problems & Imaging, 2012, 6 (1) : 133-146. doi: 10.3934/ipi.2012.6.133 |
[16] |
M. Mahalingam, Parag Ravindran, U. Saravanan, K. R. Rajagopal. Two boundary value problems involving an inhomogeneous viscoelastic solid. Discrete & Continuous Dynamical Systems - S, 2017, 10 (6) : 1351-1373. doi: 10.3934/dcdss.2017072 |
[17] |
Marcelo Messias. Periodic perturbation of quadratic systems with two infinite heteroclinic cycles. Discrete & Continuous Dynamical Systems - A, 2012, 32 (5) : 1881-1899. doi: 10.3934/dcds.2012.32.1881 |
[18] |
Alina Chertock, Alexander Kurganov, Mária Lukáčová-Medvi${\rm{\check{d}}}$ová, Șeyma Nur Özcan. An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions. Kinetic & Related Models, 2019, 12 (1) : 195-216. doi: 10.3934/krm.2019009 |
[19] |
Olena Naboka. On synchronization of oscillations of two coupled Berger plates with nonlinear interior damping. Communications on Pure & Applied Analysis, 2009, 8 (6) : 1933-1956. doi: 10.3934/cpaa.2009.8.1933 |
[20] |
Longxiang Fang, Narayanaswamy Balakrishnan, Wenyu Huang. Stochastic comparisons of parallel systems with scale proportional hazards components equipped with starting devices. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2021004 |
2019 Impact Factor: 1.366
Tools
Metrics
Other articles
by authors
[Back to Top]