Abstract
A continuum model of transportation network is considered in presence of capacity constraints on the flow. The equilibrium conditions are expressed in terms of a Variational Inequality for which an existence theorem and a computational procedure are provided.
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References
J.M. Borwein-A.S. Lewis, Practical conditions for Fenchel duality in Infinite Dimensions, Pitman Research Notes in Mathematics Series 252, M.A. Théra-J.B. Baillon Editors, 83–89.
S. Dafermos, Continuum Modelling of Transportation Networks, Transportation Res. 14 B (1980), 295–301.
P. Daniele, Lagrangean Function for Dynamic Variational Inequalities, Rendiconti del Circolo Matematico di Palermo,, Serie II, 58(1999), 101–119.
P. Daniele-A. Maugeri, Vector Variational Inequalities and a Continuum Modelling of Traffic Equilibrium Problem, in Vector Variational Inequalities and Vector Equilibria, F. Giannessi Ed., Kluwer Academic Publishers (2000), 97–111.
J. Gwinner, On continuum Modelling of Large Dense Networks in Urban Road Traffic, in Mathematics in Transport Planning and Control ( J.D. Griffiths Ed.), IMA Conference, Cardiff (1988).
G. Idone, Variational Inequalities and Applications to a Continuum Model of Transportation Network with Capacity Constraints, to appear in Journal of Global Optimization, 2002.
A. Maugeri, Dynamic Models and Generalized Equilibrium Problems, in New Trends in Mathematical Programming, F. Giannessi et al. Eds., Kluwer Academis Publishers (1998), 191–202.
A. Maugeri, New Classes of Variational Inequalities anf Applications to Equilibrium Problems, Methods of Operation Research 53(1985), 129–131.
A. Maugeri, New Classes of Variational Inequalities anf Applications to Equilibrium Problems, Rendiconti Accademia Nazionale delle Scienze deta dei XL 11(1987), 224–285.
A. Maugeri, Equilibrium Problems and Variational Inequalities, in Equilibrium Problems: Nonsmooth Optimization and Variational Inequalities Models, A. Maugeri, F. Giannessi, P. Pardalos Eds., Kluwer Academic Publishers (2001), 187–205.
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Daniele, P., Idone, G., Maugeri, A. (2003). The Continuum Model of Transportation Problem. In: Daniele, P., Giannessi, F., Maugeri, A. (eds) Equilibrium Problems and Variational Models. Nonconvex Optimization and Its Applications, vol 68. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0239-1_3
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DOI: https://doi.org/10.1007/978-1-4613-0239-1_3
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