A new look at projected gradient method for equilibrium assignment

Transportation Research Record

Volumn , Issue 2090, 2009, Pages 10-16

  Florian, Michael ^a   Constantin, Isabelle ^b   Florian, Dan ^b  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b INRO Consultants   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; GRADIENT METHODS; TRAFFIC CONTROL;

ALGORITHM FOR SOLVING; COMPUTING TIME; DECOMPOSITION SCHEME; EQUILIBRIUM ASSIGNMENT; GAUSS-SEIDEL; GRADIENT ALGORITHM; LINEAR APPROXIMATION METHOD; PROJECTED GRADIENT; PROJECTED GRADIENT METHODS; TRAFFIC ASSIGNMENT;

APPROXIMATION ALGORITHMS;

EID: 76149135678     PISSN: 03611981     EISSN: None     Source Type: Journal    
DOI: 10.3141/2090-02     Document Type: Article

References (24)

1. Frank, M., and P. Wolfe. An Algorithm for Quadratic Programming. Naval Research Logistics Quarterly, Vol.3, 1956, pp. 95-110.
2. LeBlanc, L. Mathematical Programming Algorithms for Large Scale Network Equilibrium and Network Design Problems. PhD dissertation. Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Ill., 1973.
3. Nguyen, S. Une approche unifiée des méthodes d'équilibre pour l'affectation du trafic. PhD thesis. Département d'IRO, Université de Montréal, Quebec, Canada, 1974.
4. Florian, M., and S. Nguyen. An Application and Validation of Equilibrium Trip Assignment Methods. Transportation Science, Vol.10, 1976, pp. 374-389.
5. Dow, P., and D. Van Vliet. Capacity Restrained Road Assignment. Traffic Engineering Control, Vol.20, 1979, pp. 261-273.
6. Hearn, D. W., S. Lawphongpanich, and Y. A. Ventura. Restricted Simplicial Decomposition: Computation and Extensions. Mathematical Programming Study, Vol.31, 1987, pp. 99-118.
7. Florian, M., J. Guelat, and H. Spiess. An Efficient Implementation of the PARTAN Variant of the Linear Approximation Method for the Network Equilibrium Problem. Networks, Vol.17, 1987, pp. 319-339.
8. Slavin, H., J. Brandon, and A. Rabinowicz. An Empirical Comparison of Alternative User Equilibrium Traffic Assignment Methods. Presented at Association for European Transport, Conference, Leeuwenhorst, Netherlands, 2006.
9. Boyce, D., D. Ralevic-Dekic, and H. Bar-Gera. Convergence of Traffic Assignments: How Much Is Enough? Journal of Transportation Engineering ASCE, Vol.130, 2004, pp. 1-15.
10. Dafermos, S. Traffic Assignment and Resource Allocation in Transportation Networks. PhD dissertation. Johns Hopkins University, Baltimore, Md., 1968.
11. Dafermos, S., and R. Sparrow. The Traffic Assignment Problem for a General Network. Journal of Research of the National Bureau of Standards B, Vol.73, 1969, pp. 91-118.
12. Larsson, T., and M. Patriksson. Simplicial Decomposition with Disaggregate Representation for the Traffic Assignment Problem. Transportation Science, Vol.26, 1992, pp. 4-17.
13. Jayakrishnan, R., W. K. Tsai, J. Prashker, and S. Rajadhyaksha. A Faster Path-Based Algorithm for Traffic Assignment. In Transportation Research Record 1443, TRB, National Research Council, Washington, D.C., 1994, pp. 75-83.
14. Bertsekas, D. On the Goldstein-Levitin-Polyak Gradient Projection Method. IEEE Transactions on Automatic Control, Vol.21, 1976, pp. 174-184.
15. Chen, A., D.-H. Lee, and R. Jayakrishnan. Computational Study of the State-of-the-Art Path Based Traffic Assignment Algorithms. Mathematics and Computers in Simulation, Vol.59, 2002, pp. 509-518.
16. Cheng, L., Y. Iida, N. Uno, and W. Wang. Alternative Quasi-Newton Methods for Capacitated User Equilibrium Assignment. In Transportation Research Record: Journal of the Transportation Research Board, No.1857, Transportation Research Board of the National Academies, Washington, D.C., 2003, pp. 109-116.
17. Chiou, S. W. Bilevel Programming for the Continuous Transportation Network Design Problem. Transportation Research B, Vol.39, 2005, pp. 361-383.
18. Bar-Gera, H. Origin-Based Algorithms for Transportation Network Modeling. PhD thesis. University of Illinois, Chicago, 1999.
19. Bar-Gera, H. Origin-Based Algorithm for the Traffic Assignment Problem. Transportation Science, Vol.36, 2002, pp. 398-417.
20. Dial, R. A Path-Based User-Equilibrium Traffic Assignment Algorithm that Obviates Path Storage and Enumeration. Transportation Research B, Vol.40, 2006, pp. 917-936.
21. Rosen, B. The Gradient Projection Method for Nonlinear Programming, I. Linear Constraints. Journal of the Society for Industrial and Applied Mathematics, Vol.9, 1960, pp. 181-217.
22. Beckman, M., C. McGuire, and C. Winsten. Studies in the Economics of Transportation. Yale University Press, New Haven, Conn., 1956.
23. Wardrop, J. Some Theoretical Aspects of Road Traffic Research. Proceedings of the Institution of Civil Engineers, Part 2, Vol.1, 1952, pp. 325-378.
24. Luenberger, D. Linear and Nonlinear Programming, 2nd ed. Addison- Wesley, Reading, Mass., 1984.