- Previous Article
- JIMO Home
- This Issue
-
Next Article
An outcome space algorithm for minimizing the product of two convex functions over a convex set
Solving nonadditive traffic assignment problems: A self-adaptive projection-auxiliary problem method for variational inequalities
1. | School of Computer Sciences, Nanjing Normal University, Nanjing 210097 |
2. | School of Mathematical Science, Nanjing Normal University, Nanjing 210046 |
3. | School of Mathematical Sciences, Key Laboratory for NSLSCS of Jiangsu Province, Nanjing Normal University, Nanjing 210046, China |
4. | Department of Civil Engineering, The Hong Kong University of Science and Technology, Hong Kong |
References:
[1] |
R. P. Agdeppa, N. Yamashita and M. Fukushima, The traffic equilibrium problem with nonadditive costs and its monotone mixed complementarity problem formulation,, Transportation Research Part B, 41 (2007), 862.
doi: 10.1016/j.trb.2007.04.008. |
[2] |
D. Bernstein and S. Gabriel, Solving the non-additive traffic equilibrium problem,, in, (1997), 72.
|
[3] |
D. P. Bertsekas and E. M. Gafni, Projection method for variational inequalities with application to the traffic assignment problem,, Mathematical Programming Study, 17 (1982), 139.
doi: 10.1007/BFb0120965. |
[4] |
A. Bnouhachem, M. H. Xu, X. L. Fu and Z. H. Sheng, Modified extragradient methods for solving variational inequalities,, Computers and Mathematics with Applications, 57 (2009), 230.
doi: 10.1016/j.camwa.2008.10.065. |
[5] |
G. Cohen, Auxiliary problem principle extended to variational inequalities,, Journal of Optimization Theory and Applications, 59 (1988), 325.
|
[6] |
T. De Luca, F. Facchinei and C. Kanzow, A theoretical and numerical comparison of some semismooth algorithms for complementarity problems,, Computational Optimization and Applications, 16 (2000), 173.
doi: 10.1023/A:1008705425484. |
[7] |
B. C. Eaves, On the basic theorem of complementarity,, Mathematical Programming, 1 (1971), 68.
doi: 10.1007/BF01584073. |
[8] |
F. Facchinei and J. S. Pang, "Finite-Dimensional Variational Inequalities and Complementarity Problems,", Volumes I and II, (2003).
|
[9] |
M. C. Ferris and J. S. Pang, Engineering and economic applications of complementarity problems,, SIAM Review, 39 (1997), 669.
doi: 10.1137/S0036144595285963. |
[10] |
S. Gabriel and D. Bernstein, The traffic equilibrium problem with non-additive path costs,, Transportation Science, 31 (1997), 337.
doi: 10.1287/trsc.31.4.337. |
[11] |
A. A. Goldstein, Convex programming in Hilbert space,, Bulletin of the American Mathematical Society, 70 (1964), 709.
doi: 10.1090/S0002-9904-1964-11178-2. |
[12] |
D. R. Han and Hong K. Lo, Solving non-additive traffic assignment problems: A descent method for co-coercive variational inequalities,, European Journal of Operational Research, 159 (2004), 529.
doi: 10.1016/S0377-2217(03)00423-5. |
[13] |
D. R. Han and W. Y. Sun, A new modified Goldstein-Levitin-Polyak projection method for variational inequality problems,, Computers and Mathematics with Applications, 47 (2004), 1817.
doi: 10.1016/j.camwa.2003.12.002. |
[14] |
D. R. Han, Inexact operator splitting methods with self-adaptive strategy for variational inequality problems,, Journal of Optimization Theory and Applications, 132 (2007), 227.
doi: 10.1007/s10957-006-9060-5. |
[15] |
D. R. Han, W. Xu and H. Yang, An operator splitting method for variational inequalities with partially unknown mappings,, Numerische Mathematik, 111 (2008), 207.
doi: 10.1007/s00211-008-0181-7. |
[16] |
P. T. Harker and J. S. Pang, Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications,, Mathematical Programming, 48 (1990), 161.
doi: 10.1007/BF01582255. |
[17] |
B. S. He, A class of projection and contraction methods for monotone variational inequalities,, Applied Mathematics and Optimization, 35 (1997), 69.
|
[18] |
B. S. He, H. Yang, Q. Meng and D. R. Han, Modified Goldstein-Levitin-Polyak projection method for asymmetric strongly monotone variational inequalities,, Journal of Optimization Theory and Applications, 112 (2002), 129.
doi: 10.1023/A:1013048729944. |
[19] |
B. S. He, L. Z. Liao and S. L. Wang, Self-adaptive operator splitting methods for monotone variational inequalities,, Numerische Mathematik, 94 (2003), 715.
|
[20] |
B. S. He, X. H. Liu, T. Wu and X. Z. He, Self-adaptive projection method for co-coercive variational inequalities,, European Journal of Operational Research, 196 (2009), 43.
doi: 10.1016/j.ejor.2008.03.004. |
[21] |
G. M. Korpolevich, The extragradient method for finding saddle points and other problems,, Matecon, 12 (1976), 747.
|
[22] |
E. N. Khobotov, Modification of the extragradient method for solving variational inequalities and certain optimization problems,, USSR, 27 (1987), 120.
doi: 10.1016/0041-5553(87)90058-9. |
[23] |
E. S. Levitin and B. T. Polyak, Constrained minimization problems,, USSR. Computational Mathematics and Mathematical Physics, 6 (1966), 1.
doi: 10.1016/0041-5553(66)90114-5. |
[24] |
H. Lo, A dynamic traffic assignment formulation that encapsulates the Cell Transmission Model,, in, (1999), 327. Google Scholar |
[25] |
H. Lo and A. Chen, Reformulating the traffic equilibrium problem via a smooth gap function,, Mathematical and Computer Modeling, 31 (2000), 179.
doi: 10.1016/S0895-7177(99)00231-9. |
[26] |
H. Lo and A. Chen, Traffic equilibrium problem with route-specific costs: Formulation and algorithms,, Transportation Research Part B, 34 (2000), 493.
doi: 10.1016/S0191-2615(99)00035-1. |
[27] |
A. Nagurney, "Network Economics: A Variational Inequality Approach,", Kluwer Academics Publishers, (1993).
|
[28] |
K. Scott and D. Bernstein, Solving a traffic equilibrium problem when path costs are non-additive,, Paper presented at, (1999). Google Scholar |
[29] |
K. Taji, M. Fukushima and T. Ibaraki, A globally convergent Newton method for solving strongly monotone variational inequalities,, Mathematical Programming, 58 (1993), 369.
doi: 10.1007/BF01581276. |
[30] |
J. G. Wardrop, Some theoretical aspects of road traffic research,, in, 1 (1952), 325. Google Scholar |
[31] |
H. Yang, Q. Meng and D. H. Lee, Trial-and-error implementation of marginal-cost pricing on networks in the absence of demand functions,, Transportation Research Part B, 38 (2004), 477.
doi: 10.1016/S0191-2615(03)00077-8. |
[32] |
D. L. Zhu and P. Marcotte, Co-coercivity and its role in the convergence of iterative schemes for solving variational inequalities,, SIAM Journal on Optimization, 6 (1996), 714.
doi: 10.1137/S1052623494250415. |
[33] |
T. Zhu and Z. G. Yu, A simple proof for some important properties of the projection mapping,, Mathematical Inequalities and Applicatrions, 7 (2004), 453.
doi: 10.7153/mia-07-45. |
show all references
References:
[1] |
R. P. Agdeppa, N. Yamashita and M. Fukushima, The traffic equilibrium problem with nonadditive costs and its monotone mixed complementarity problem formulation,, Transportation Research Part B, 41 (2007), 862.
doi: 10.1016/j.trb.2007.04.008. |
[2] |
D. Bernstein and S. Gabriel, Solving the non-additive traffic equilibrium problem,, in, (1997), 72.
|
[3] |
D. P. Bertsekas and E. M. Gafni, Projection method for variational inequalities with application to the traffic assignment problem,, Mathematical Programming Study, 17 (1982), 139.
doi: 10.1007/BFb0120965. |
[4] |
A. Bnouhachem, M. H. Xu, X. L. Fu and Z. H. Sheng, Modified extragradient methods for solving variational inequalities,, Computers and Mathematics with Applications, 57 (2009), 230.
doi: 10.1016/j.camwa.2008.10.065. |
[5] |
G. Cohen, Auxiliary problem principle extended to variational inequalities,, Journal of Optimization Theory and Applications, 59 (1988), 325.
|
[6] |
T. De Luca, F. Facchinei and C. Kanzow, A theoretical and numerical comparison of some semismooth algorithms for complementarity problems,, Computational Optimization and Applications, 16 (2000), 173.
doi: 10.1023/A:1008705425484. |
[7] |
B. C. Eaves, On the basic theorem of complementarity,, Mathematical Programming, 1 (1971), 68.
doi: 10.1007/BF01584073. |
[8] |
F. Facchinei and J. S. Pang, "Finite-Dimensional Variational Inequalities and Complementarity Problems,", Volumes I and II, (2003).
|
[9] |
M. C. Ferris and J. S. Pang, Engineering and economic applications of complementarity problems,, SIAM Review, 39 (1997), 669.
doi: 10.1137/S0036144595285963. |
[10] |
S. Gabriel and D. Bernstein, The traffic equilibrium problem with non-additive path costs,, Transportation Science, 31 (1997), 337.
doi: 10.1287/trsc.31.4.337. |
[11] |
A. A. Goldstein, Convex programming in Hilbert space,, Bulletin of the American Mathematical Society, 70 (1964), 709.
doi: 10.1090/S0002-9904-1964-11178-2. |
[12] |
D. R. Han and Hong K. Lo, Solving non-additive traffic assignment problems: A descent method for co-coercive variational inequalities,, European Journal of Operational Research, 159 (2004), 529.
doi: 10.1016/S0377-2217(03)00423-5. |
[13] |
D. R. Han and W. Y. Sun, A new modified Goldstein-Levitin-Polyak projection method for variational inequality problems,, Computers and Mathematics with Applications, 47 (2004), 1817.
doi: 10.1016/j.camwa.2003.12.002. |
[14] |
D. R. Han, Inexact operator splitting methods with self-adaptive strategy for variational inequality problems,, Journal of Optimization Theory and Applications, 132 (2007), 227.
doi: 10.1007/s10957-006-9060-5. |
[15] |
D. R. Han, W. Xu and H. Yang, An operator splitting method for variational inequalities with partially unknown mappings,, Numerische Mathematik, 111 (2008), 207.
doi: 10.1007/s00211-008-0181-7. |
[16] |
P. T. Harker and J. S. Pang, Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications,, Mathematical Programming, 48 (1990), 161.
doi: 10.1007/BF01582255. |
[17] |
B. S. He, A class of projection and contraction methods for monotone variational inequalities,, Applied Mathematics and Optimization, 35 (1997), 69.
|
[18] |
B. S. He, H. Yang, Q. Meng and D. R. Han, Modified Goldstein-Levitin-Polyak projection method for asymmetric strongly monotone variational inequalities,, Journal of Optimization Theory and Applications, 112 (2002), 129.
doi: 10.1023/A:1013048729944. |
[19] |
B. S. He, L. Z. Liao and S. L. Wang, Self-adaptive operator splitting methods for monotone variational inequalities,, Numerische Mathematik, 94 (2003), 715.
|
[20] |
B. S. He, X. H. Liu, T. Wu and X. Z. He, Self-adaptive projection method for co-coercive variational inequalities,, European Journal of Operational Research, 196 (2009), 43.
doi: 10.1016/j.ejor.2008.03.004. |
[21] |
G. M. Korpolevich, The extragradient method for finding saddle points and other problems,, Matecon, 12 (1976), 747.
|
[22] |
E. N. Khobotov, Modification of the extragradient method for solving variational inequalities and certain optimization problems,, USSR, 27 (1987), 120.
doi: 10.1016/0041-5553(87)90058-9. |
[23] |
E. S. Levitin and B. T. Polyak, Constrained minimization problems,, USSR. Computational Mathematics and Mathematical Physics, 6 (1966), 1.
doi: 10.1016/0041-5553(66)90114-5. |
[24] |
H. Lo, A dynamic traffic assignment formulation that encapsulates the Cell Transmission Model,, in, (1999), 327. Google Scholar |
[25] |
H. Lo and A. Chen, Reformulating the traffic equilibrium problem via a smooth gap function,, Mathematical and Computer Modeling, 31 (2000), 179.
doi: 10.1016/S0895-7177(99)00231-9. |
[26] |
H. Lo and A. Chen, Traffic equilibrium problem with route-specific costs: Formulation and algorithms,, Transportation Research Part B, 34 (2000), 493.
doi: 10.1016/S0191-2615(99)00035-1. |
[27] |
A. Nagurney, "Network Economics: A Variational Inequality Approach,", Kluwer Academics Publishers, (1993).
|
[28] |
K. Scott and D. Bernstein, Solving a traffic equilibrium problem when path costs are non-additive,, Paper presented at, (1999). Google Scholar |
[29] |
K. Taji, M. Fukushima and T. Ibaraki, A globally convergent Newton method for solving strongly monotone variational inequalities,, Mathematical Programming, 58 (1993), 369.
doi: 10.1007/BF01581276. |
[30] |
J. G. Wardrop, Some theoretical aspects of road traffic research,, in, 1 (1952), 325. Google Scholar |
[31] |
H. Yang, Q. Meng and D. H. Lee, Trial-and-error implementation of marginal-cost pricing on networks in the absence of demand functions,, Transportation Research Part B, 38 (2004), 477.
doi: 10.1016/S0191-2615(03)00077-8. |
[32] |
D. L. Zhu and P. Marcotte, Co-coercivity and its role in the convergence of iterative schemes for solving variational inequalities,, SIAM Journal on Optimization, 6 (1996), 714.
doi: 10.1137/S1052623494250415. |
[33] |
T. Zhu and Z. G. Yu, A simple proof for some important properties of the projection mapping,, Mathematical Inequalities and Applicatrions, 7 (2004), 453.
doi: 10.7153/mia-07-45. |
[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] |
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 |
[3] |
Qiang Guo, Dong Liang. An adaptive wavelet method and its analysis for parabolic equations. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 327-345. doi: 10.3934/naco.2013.3.327 |
[4] |
Alexandr Mikhaylov, Victor Mikhaylov. Dynamic inverse problem for Jacobi matrices. Inverse Problems & Imaging, 2019, 13 (3) : 431-447. doi: 10.3934/ipi.2019021 |
[5] |
Hildeberto E. Cabral, Zhihong Xia. Subharmonic solutions in the restricted three-body problem. Discrete & Continuous Dynamical Systems - A, 1995, 1 (4) : 463-474. doi: 10.3934/dcds.1995.1.463 |
[6] |
Deren Han, Zehui Jia, Yongzhong Song, David Z. W. Wang. An efficient projection method for nonlinear inverse problems with sparsity constraints. Inverse Problems & Imaging, 2016, 10 (3) : 689-709. doi: 10.3934/ipi.2016017 |
[7] |
Boris Kramer, John R. Singler. A POD projection method for large-scale algebraic Riccati equations. Numerical Algebra, Control & Optimization, 2016, 6 (4) : 413-435. doi: 10.3934/naco.2016018 |
[8] |
Michel Chipot, Mingmin Zhang. On some model problem for the propagation of interacting species in a special environment. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020401 |
[9] |
Fritz Gesztesy, Helge Holden, Johanna Michor, Gerald Teschl. The algebro-geometric initial value problem for the Ablowitz-Ladik hierarchy. Discrete & Continuous Dynamical Systems - A, 2010, 26 (1) : 151-196. doi: 10.3934/dcds.2010.26.151 |
[10] |
Gloria Paoli, Gianpaolo Piscitelli, Rossanno Sannipoli. A stability result for the Steklov Laplacian Eigenvalue Problem with a spherical obstacle. Communications on Pure & Applied Analysis, 2021, 20 (1) : 145-158. doi: 10.3934/cpaa.2020261 |
[11] |
Rongchang Liu, Jiangyuan Li, Duokui Yan. New periodic orbits in the planar equal-mass three-body problem. Discrete & Continuous Dynamical Systems - A, 2018, 38 (4) : 2187-2206. doi: 10.3934/dcds.2018090 |
[12] |
Sergi Simon. Linearised higher variational equations. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4827-4854. doi: 10.3934/dcds.2014.34.4827 |
[13] |
Junichi Minagawa. On the uniqueness of Nash equilibrium in strategic-form games. Journal of Dynamics & Games, 2020, 7 (2) : 97-104. doi: 10.3934/jdg.2020006 |
[14] |
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 |
[15] |
Zhihua Zhang, Naoki Saito. PHLST with adaptive tiling and its application to antarctic remote sensing image approximation. Inverse Problems & Imaging, 2014, 8 (1) : 321-337. doi: 10.3934/ipi.2014.8.321 |
[16] |
Bin Pei, Yong Xu, Yuzhen Bai. Convergence of p-th mean in an averaging principle for stochastic partial differential equations driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 1141-1158. doi: 10.3934/dcdsb.2019213 |
[17] |
Thomas Y. Hou, Ruo Li. Nonexistence of locally self-similar blow-up for the 3D incompressible Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2007, 18 (4) : 637-642. doi: 10.3934/dcds.2007.18.637 |
[18] |
Teddy Pichard. A moment closure based on a projection on the boundary of the realizability domain: 1D case. Kinetic & Related Models, 2020, 13 (6) : 1243-1280. doi: 10.3934/krm.2020045 |
[19] |
Tao Wu, Yu Lei, Jiao Shi, Maoguo Gong. An evolutionary multiobjective method for low-rank and sparse matrix decomposition. Big Data & Information Analytics, 2017, 2 (1) : 23-37. doi: 10.3934/bdia.2017006 |
[20] |
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 |
2019 Impact Factor: 1.366
Tools
Metrics
Other articles
by authors
[Back to Top]