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English version: Journal of Applied and Industrial Mathematics, 2020, 14:1, 92-103 |
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Volume 27, No 1, 2020, P. 43-60 UDC 519.8
Keywords: network equilibrium problem, partial linearization method, descent direction, inexact solution. DOI: 10.33048/daio.2020.27.658 Igor’ V. Konnov 1 Received April 23, 2019 References[1] S. Dafermos, Traffic equilibrium and variational inequalities, Transp. Sci. 14 (1), 42–54 (1980).[2] S. Dafermos, The general multimodal network equilibrium problem with elastic demand, Networks 12 (1), 57–72 (1982). [3] A. Nagurney, Network Economics: A Variational Inequality Approach (Kluwer Acad. Publ., Dordrecht, 1999). [4] M. Patriksson, The Traffic Assignment Problem: Models and Methods (Dover, Mineola, NY, 2015). [5] T. L. Magnanti, Models and algorithms for predicting urban traffic equilibria, in Transportation Planning Models (North–Holland, Amsterdam, 1984), pp. 153–185. [6] I. Konnov and O. Pinyagina, Partial linearization method for network equilibrium problems with elastic demands, in Discrete Optimization and Op?erations Research (Proc. 9th Int. Conf. DOOR-2016, Vladivostok, Russia,Sept. 19–23, 2016) (Springer, Heidelberg, 2016), pp. 418–429. [7] I. V. Konnov, Simplified versions of the conditional gradient method, Optimization 67 (12), 2275–2290 (2018). [8] H. Mine and M. Fukushima, A minimization method for the sum of a convex function and a continuously differentiable function, J. Optim. Theor. Appl. 33, 9–23 (1981). [9] M. Patriksson, Cost approximation: A unified framework of descent algorithms for nonlinear programs, SIAM J. Optim. 8, 561–582 (1998). [10] M. Patriksson, Nonlinear Programming and Variational Inequality Problems: A Unified Approach (Kluwer Acad. Publ., Dordrecht, 1999). [11] K. Bredies, D. A. Lorenz, and P. Maass, A generalized conditional gradient method and its connection to an iterative shrinkage method, Comput. Optim. Appl. 42, 173–193 (2009). [12] G. Scutari, F. Facchinei, P. Song, D. P. Palomar, and J.-S. Pang, Decomposition by partial linearization: Parallel optimization of multi-agent systems, IEEE Trans. Signal Process. 62, 641-656 (2014). [13] I. V. Konnov, On auction equilibrium models with network applications, NETNOMICS: Econ. Res. Electron. Networking 16 (1), 107–125 (2015). [14] O. Pinyagina, On a network equilibrium problem with mixed demand, Discrete Optimization and Operations Research (Proc. 9th Int. Conf. DOOR-2016, Vladivostok, Russia, Sept. 19–23, 2016) (Springer, Heidelberg, 2016), pp. 578–583. [15] O. V. Pinyagina, The network equilibrium problem with mixed demand, Diskretn. Anal. Issled. Oper. 24 (4), 77–94 (2017) [J. Appl. Ind. Math. 11 (4), 554–563 (2017)]. [16] D. P. Bertsekas and E. M. Gafni, Projection methods for variational inequalities with application to the traffic assignment problem, in Nondifferential and Variational Techniques in Optimization (Springer, Heidelberg, 1982), pp. 139–159. [17] A. B. Nagurney, Comparative tests of multimodal traffic equilibrium methods, Transp. Res., Part B: Methodological 18 (1), 469–485 (1984). |
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