Abstract
We suggest a partial linearization method for network equilibrium problems with elastic demands, which can be set-valued in general. The main element of this method is a partially linearized auxiliary problem. We propose a simple solution method for the auxiliary problem, which is based on optimality conditions. This method can be viewed as alternative to the conditional gradient method for the single-valued case. Some results of preliminary calculations which confirm efficiency of the new method are also presented.
In this work, the authors were supported by Russian Foundation for Basic Research, project No 16-01-00109. The first author was also supported by grant No 297689 from Academy of Finland.
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References
Fukushima, M., Mine, H.: A generalized proximal point algorithm for certain non-convex minimization problems. Int. J. Syst. Sci. 12, 989–1000 (1981)
Mine, H., Fukushima, M.: A minimization method for the sum of a convex function and a continuously differentiable function. J. Optim. Theor. Appl. 33, 9–23 (1981)
Patriksson, M.: Nonlinear Programming and Variational Inequality Problems: a Unified Approach. Kluwer, Dordrecht (1999)
Frank, M., Wolfe, P.: An algorithm for quadratic programming. Nav. Res. Logistics Q. 3, 95–110 (1956)
Levitin, E.S., Polyak, B.T.: Constrained minimization methods. USSR Comput. Math. Math. Phys. 6(5), 1–50 (1966)
Magnanti, T.L.: Models and Algorithms for Predicting Urban Traffic Equilibria. In: Florian, M. (ed.) Transportation Planning Models, pp. 153–185. North-Holland, Amsterdam (1984)
Patriksson, M.: The Traffic Assignment Problem. Models and Methods. VSP, Utrecht (1994)
Nagurney, A.: Network Economics: A Variational Inequality Approach. Kluwer, Dordrecht (1999)
Konnov, I.V.: On Auction Equilibrium Models with Network Applications. Netnomics 16, 107–125 (2015)
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Konnov, I., Pinyagina, O. (2016). Partial Linearization Method for Network Equilibrium Problems with Elastic Demands. In: Kochetov, Y., Khachay, M., Beresnev, V., Nurminski, E., Pardalos, P. (eds) Discrete Optimization and Operations Research. DOOR 2016. Lecture Notes in Computer Science(), vol 9869. Springer, Cham. https://doi.org/10.1007/978-3-319-44914-2_33
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DOI: https://doi.org/10.1007/978-3-319-44914-2_33
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