Geodesic
Inexact partial linearization methods for~network equilibrium problems
Diskretnyj analiz i issledovanie operacij, Tome 27 (2020) no. 1, pp. 43-60.

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We propose some simplified modifications of the partial linearization method for network equilibrium problems with mixed demand. In these modifications, the auxiliary direction choice problem is solved approximately. In the modifications, the basic convergence properties of the original method are preserved, while the inexact solution of the auxiliary problems reduces the computational efforts. Preliminary numerical tests show the advantages and efficiency of our approach as compared with the exact variant of the method. Tab. 3, illustr. 2, bibliogr. 17.
Keywords: network equilibrium problem, partial linearization method
Mots-clés : descent direction, inexact solution. 
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I. V. Konnov; E. Laitinen; O. V. Pinyagina. Inexact partial linearization methods for~network equilibrium problems. Diskretnyj analiz i issledovanie operacij, Tome 27 (2020) no. 1, pp. 43-60. http://geodesic.mathdoc.fr/item/DA_2020_27_1_a2/

[1] S. Dafermos, “Traffic equilibrium and variational inequalities”, Transp. Sci., 14:1 (1980), 42–54 | DOI | MR

[2] S. Dafermos, “The general multimodal network equilibrium problem with elastic demand”, Networks, 12:1 (1982), 57–72 | DOI | MR | Zbl

[3] A. Nagurney, Network economics: A variational inequality approach, Kluwer Acad. Publ., Dordrecht, 1999, 444 pp. | MR

[4] M. Patriksson, The traffic assignment problem: models and methods, Dover Publ., Mineola, NY, 2015, 240 pp.

[5] T. L. Magnanti, “Models and algorithms for predicting urban traffic equilibria”, Transportation Planning Models, North-Holland, Amsterdam, 1984, 153–185

[6] I. V. Konnov, O. V. Pinyagina, “Partial linearization method for network equilibrium problems with elastic demands”, Discrete Optimization and Operations Research, DOOR 2016, Proc. 9th Int. Conf. (Vladivostok, Russia, Sep. 19–23, 2016), Lect. Notes Comput. Sci., 9869, Springer, Heidelberg, 2016, 418–429 | DOI | MR | Zbl

[7] I. V. Konnov, “Simplified versions of the conditional gradient method”, Optimization, 67:12 (2018), 2275–2290 | DOI | MR | Zbl

[8] H. Mine, M. Fukushima, “A minimization method for the sum of a convex function and a continuously differentiable function”, J. Optim. Theor. Appl., 33 (1981), 9–23 | DOI | MR | Zbl

[9] M. Patriksson, “Cost approximation: A unified framework of descent algorithms for nonlinear programs”, SIAM J. Optim., 8 (1998), 561–582 | DOI | MR | Zbl

[10] M. Patriksson, Nonlinear programming and variational inequality problems: A unified approach, Kluwer, Dordrecht, 1999, 348 pp. | MR | Zbl

[11] K. Bredies, D. A. Lorenz, P. Maass, “A generalized conditional gradient method and its connection to an iterative shrinkage method”, Comput. Optim. Appl., 42 (2009), 173–193 | DOI | MR | Zbl

[12] G. Scutari, F. Facchinei, P. Song, D. P. Palomar, J. S. Pang, “Decomposition by partial linearization: Parallel optimization of multi-agent systems”, IEEE Trans. Signal Process, 62 (2014), 641–656 | DOI | MR | Zbl

[13] I. V. Konnov, “On auction equilibrium models with network applications”, NETNOMICS: Economic Research and Electronic Networking, 16:1 (2015), 107–125 | DOI

[14] O. V. Pinyagina, “On a network equilibrium problem with mixed demand”, Discrete Optimization and Operations Research, DOOR 2016, Proc. 9th Int. Conf. (Vladivostok, Russia, Sep. 19–23, 2016), Lect. Notes Comput. Sci., 9869, Springer, Heidelberg, 2016, 578–583 | DOI | MR | Zbl

[15] O. V. Pinyagina, “The network equilibrium problem with mixed demand”, J. Appl. Ind. Math., 11:4 (2017), 554–563 | DOI | MR | Zbl

[16] D. P. Bertsekas, E. M. Gafni, “Projection methods for variational inequalities with application to the traffic assignment problem”, Nondifferential and Variational Techniques in Optimization, Springer, Heidelberg, 1982, 139–159 | DOI | MR

[17] A. B. Nagurney, “Comparative tests of multimodal traffic equilibrium methods”, Transp. Res., Part B: Methodological, 18:1 (1984), 469–485 | DOI