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Polymorphic uncertain nonlinear programming model and algorithm for maximizing the fatigue life of V-belt drive
A Stackelberg game management model of the urban public transport
1. | School of Mathematical Sciences, Qufu Normal University, Qufu Shandong, 273165, China |
2. | School of Traffic and Transportation, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China |
3. | School of Management Science, Qufu Normal University, Rizhao Shandong, 276800 |
References:
[1] |
M. S. Bazaraa, H. D. Sherali and C. M. Shetty, Second edition, "Nonlinear Programming: Theory and Algorithms," Wiley, New York, 1993. |
[2] |
A. Bensoussan, Points de Nash dans le cas de fonctionnelles quadratiques et jeux différentials linéaires à $N$ personnes, SIAM Journal Control, 12 (1974), 460-499.
doi: 10.1137/0312037. |
[3] |
D. P. Bertsekas, "Constrained Optimization and Lagrange Multiplier Methods," Computer Science and Applied Mathematics, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1982. |
[4] |
T. Boulogne, E. Altman, H. Kameda and O. Pourtallier, Mixed equilibrium (ME) for multi-class routing games, IEEE Transactions on Automatic Control, 47 (2002), 903-916.
doi: 10.1109/TAC.2002.1008357. |
[5] |
W.-K. Ching, S.-M. Choi and M. Huang, Optimal service capacity in a multiple-server queueing system: A game theory approach, Journal of Industrial and Management Optimization, 6 (2010), 73-102. |
[6] |
M. Fukushima, Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems, Mathematical Programming, 53 (1992), 99-110.
doi: 10.1007/BF01585696. |
[7] |
P. T. Harker, Generalized Nash games and quasi-variational inequalities, European Journal of Operational Research, 54 (1991), 81-94.
doi: 10.1016/0377-2217(91)90325-P. |
[8] |
P. T. Harker, Multiple equilibrium behaviors on networks, Transportation Science, 22 (1988), 39-46.
doi: 10.1287/trsc.22.1.39. |
[9] |
B.-S. He, H. Yang and C.-S. Zhang, A modified augmented Lagrangian method for a class of monotone variational inequalities, European Journal of Operational Research, 159 (2004), 35-51.
doi: 10.1016/S0377-2217(03)00385-0. |
[10] |
D. W. Hearn and M. V. Ramana, Solving congestion toll pricing models, in "Equilibrium and Advanced Transportation Modeling" (eds. P. Marcotte and S. Nguyen), Kluwer Academic Publishers, (1998), 109-124. |
[11] |
O. Kofi and I. Ugboro, Effective strategic planning in public transit systems, Transportation Research Part E, 44 (2008), 420-439.
doi: 10.1016/j.tre.2006.10.008. |
[12] |
R. J. La and V. Anantharam, Optimal routing control: Repeated game approach, IEEE Transactions on Automatic Control, 47 (2002), 437-450.
doi: 10.1109/9.989076. |
[13] |
G. Laporte, J. A. Mesa and P. Federico, A game theoretic frame work for the robust railway transit network design problem, Transportation Research Part B, 44 (2010), 447-459.
doi: 10.1016/j.trb.2009.08.004. |
[14] |
Z.-Q. Luo, J.-S. Pang and D. Ralph, "Mathematical Programs with Equilibrium Constraints," Cambridge University Press, Cambridge, 1996.
doi: 10.1017/CBO9780511983658. |
[15] |
Q. Meng, H. Yang and M. G. H. Bell, An equivalent continuously differentiable model and a locally convergent algorithm for the continuous network design problem, Transportation Research Part B, 35 (2001), 83-105.
doi: 10.1016/S0191-2615(00)00016-3. |
[16] |
Y. Nie, H. M. Zhang and D. H. Lee, Models and algorithms for the traffic assignment problem with link capacity constraints, Transportation Research Part B, 38 (2004), 285-312.
doi: 10.1016/S0191-2615(03)00010-9. |
[17] |
J. S. Pang, The generalized quasi-variational inequality problem, Mathematics of Operations Research, 7 (1982), 211-222.
doi: 10.1287/moor.7.2.211. |
[18] |
M. Patriksson and R. T. Rockafellar, A mathematical model and descent algorithm for bilevel traffic management, Transportation Science, 36 (2002), 271-291.
doi: 10.1287/trsc.36.3.271.7826. |
[19] |
K. Shimizu, Y. Ishizuka and J. F. Bard, "Non-Differentiable and Two-Level Mathematical Programming," Kluwer Academic Publishers, Boston, MA, 1997. |
[20] |
L. J. Sun and Z. Y. Gao, An equilibrium model for urban transit assignment based on game theory, European Journal of Operational Research, 181 (2007), 305-314.
doi: 10.1016/j.ejor.2006.05.028. |
[21] |
T. Van Vuren, D. Van Vliet and M. Smith, Combined equilibrium in a network with partial route guidance, in "Traffic Control Methods" (eds. S. Yagar and S. E. Rowen), Engineering Foundation Press, New York, (1990), 375-387. |
[22] |
T. Van Vuren and D. Watling, A multiple user class assignment model for route guidance, Transportation Research Record, 1306 (1991), 22-31. |
[23] |
Q.-Y. Yan, J.-B. Li and J.-L. Zhang, Licensing schemes in Stackelberg model under asymmetric information of product costs, Journal of Industrial and Management Optimization, 3 (2007), 763-774.
doi: 10.3934/jimo.2007.3.763. |
[24] |
H. Yang, X. N. Zhang and Q. Meng, Modeling private highways in networks with entry-exit based toll charges, Transportation Research Part B, 38 (2004), 191-213.
doi: 10.1016/S0191-2615(03)00050-X. |
[25] |
H. Yang, X. N. Zhang and Q. Meng, Stackelberg games and multiple equilibrium behaviors on networks, Transportation Research Part B, 41 (2007), 841-861.
doi: 10.1016/j.trb.2007.03.002. |
[26] |
J. Zhou, W. H. K. Lam and B. Heydecker, The generalized Nash equilibrium model for oligopolistic transit market with elastic demand, Transportation Research Part B, 39 (2005), 519-544.
doi: 10.1016/j.trb.2004.07.003. |
[27] |
D. Zhu and P. Marcotte, Modified descent methods for solving the monotone variational inequality problem, Operations Research Letters, 14 (1993), 111-120.
doi: 10.1016/0167-6377(93)90103-N. |
show all references
References:
[1] |
M. S. Bazaraa, H. D. Sherali and C. M. Shetty, Second edition, "Nonlinear Programming: Theory and Algorithms," Wiley, New York, 1993. |
[2] |
A. Bensoussan, Points de Nash dans le cas de fonctionnelles quadratiques et jeux différentials linéaires à $N$ personnes, SIAM Journal Control, 12 (1974), 460-499.
doi: 10.1137/0312037. |
[3] |
D. P. Bertsekas, "Constrained Optimization and Lagrange Multiplier Methods," Computer Science and Applied Mathematics, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1982. |
[4] |
T. Boulogne, E. Altman, H. Kameda and O. Pourtallier, Mixed equilibrium (ME) for multi-class routing games, IEEE Transactions on Automatic Control, 47 (2002), 903-916.
doi: 10.1109/TAC.2002.1008357. |
[5] |
W.-K. Ching, S.-M. Choi and M. Huang, Optimal service capacity in a multiple-server queueing system: A game theory approach, Journal of Industrial and Management Optimization, 6 (2010), 73-102. |
[6] |
M. Fukushima, Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems, Mathematical Programming, 53 (1992), 99-110.
doi: 10.1007/BF01585696. |
[7] |
P. T. Harker, Generalized Nash games and quasi-variational inequalities, European Journal of Operational Research, 54 (1991), 81-94.
doi: 10.1016/0377-2217(91)90325-P. |
[8] |
P. T. Harker, Multiple equilibrium behaviors on networks, Transportation Science, 22 (1988), 39-46.
doi: 10.1287/trsc.22.1.39. |
[9] |
B.-S. He, H. Yang and C.-S. Zhang, A modified augmented Lagrangian method for a class of monotone variational inequalities, European Journal of Operational Research, 159 (2004), 35-51.
doi: 10.1016/S0377-2217(03)00385-0. |
[10] |
D. W. Hearn and M. V. Ramana, Solving congestion toll pricing models, in "Equilibrium and Advanced Transportation Modeling" (eds. P. Marcotte and S. Nguyen), Kluwer Academic Publishers, (1998), 109-124. |
[11] |
O. Kofi and I. Ugboro, Effective strategic planning in public transit systems, Transportation Research Part E, 44 (2008), 420-439.
doi: 10.1016/j.tre.2006.10.008. |
[12] |
R. J. La and V. Anantharam, Optimal routing control: Repeated game approach, IEEE Transactions on Automatic Control, 47 (2002), 437-450.
doi: 10.1109/9.989076. |
[13] |
G. Laporte, J. A. Mesa and P. Federico, A game theoretic frame work for the robust railway transit network design problem, Transportation Research Part B, 44 (2010), 447-459.
doi: 10.1016/j.trb.2009.08.004. |
[14] |
Z.-Q. Luo, J.-S. Pang and D. Ralph, "Mathematical Programs with Equilibrium Constraints," Cambridge University Press, Cambridge, 1996.
doi: 10.1017/CBO9780511983658. |
[15] |
Q. Meng, H. Yang and M. G. H. Bell, An equivalent continuously differentiable model and a locally convergent algorithm for the continuous network design problem, Transportation Research Part B, 35 (2001), 83-105.
doi: 10.1016/S0191-2615(00)00016-3. |
[16] |
Y. Nie, H. M. Zhang and D. H. Lee, Models and algorithms for the traffic assignment problem with link capacity constraints, Transportation Research Part B, 38 (2004), 285-312.
doi: 10.1016/S0191-2615(03)00010-9. |
[17] |
J. S. Pang, The generalized quasi-variational inequality problem, Mathematics of Operations Research, 7 (1982), 211-222.
doi: 10.1287/moor.7.2.211. |
[18] |
M. Patriksson and R. T. Rockafellar, A mathematical model and descent algorithm for bilevel traffic management, Transportation Science, 36 (2002), 271-291.
doi: 10.1287/trsc.36.3.271.7826. |
[19] |
K. Shimizu, Y. Ishizuka and J. F. Bard, "Non-Differentiable and Two-Level Mathematical Programming," Kluwer Academic Publishers, Boston, MA, 1997. |
[20] |
L. J. Sun and Z. Y. Gao, An equilibrium model for urban transit assignment based on game theory, European Journal of Operational Research, 181 (2007), 305-314.
doi: 10.1016/j.ejor.2006.05.028. |
[21] |
T. Van Vuren, D. Van Vliet and M. Smith, Combined equilibrium in a network with partial route guidance, in "Traffic Control Methods" (eds. S. Yagar and S. E. Rowen), Engineering Foundation Press, New York, (1990), 375-387. |
[22] |
T. Van Vuren and D. Watling, A multiple user class assignment model for route guidance, Transportation Research Record, 1306 (1991), 22-31. |
[23] |
Q.-Y. Yan, J.-B. Li and J.-L. Zhang, Licensing schemes in Stackelberg model under asymmetric information of product costs, Journal of Industrial and Management Optimization, 3 (2007), 763-774.
doi: 10.3934/jimo.2007.3.763. |
[24] |
H. Yang, X. N. Zhang and Q. Meng, Modeling private highways in networks with entry-exit based toll charges, Transportation Research Part B, 38 (2004), 191-213.
doi: 10.1016/S0191-2615(03)00050-X. |
[25] |
H. Yang, X. N. Zhang and Q. Meng, Stackelberg games and multiple equilibrium behaviors on networks, Transportation Research Part B, 41 (2007), 841-861.
doi: 10.1016/j.trb.2007.03.002. |
[26] |
J. Zhou, W. H. K. Lam and B. Heydecker, The generalized Nash equilibrium model for oligopolistic transit market with elastic demand, Transportation Research Part B, 39 (2005), 519-544.
doi: 10.1016/j.trb.2004.07.003. |
[27] |
D. Zhu and P. Marcotte, Modified descent methods for solving the monotone variational inequality problem, Operations Research Letters, 14 (1993), 111-120.
doi: 10.1016/0167-6377(93)90103-N. |
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