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Variational Inequalities and Applications to a Continuum Model of Transportation Network with Capacity Constraints

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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 is provided.

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References

  1. Borwein, J.W. and Lewis, A.S. Practical Conditions for Fenchel Duality in Infinite Dimensions, in: Théra, M.A. and Baillon, J.B. (eds), Pitman Research Notes in Mathematics Series 252, 83–89.

  2. Dafermos, S. (1980), Continuum Modelling of Transportation Networks, Transportation Res. 14 B, 295–301.

    Google Scholar 

  3. Daniele, P. (1999), Lagrangean Function for Dynamic Variational Inequalities, Rendiconti del Circolo Matematico di Palermo, Serie II 58, 101–119.

    Google Scholar 

  4. Daniele, P. and Maugeri, A. (2000), Vector Variational Inequalities and a Continuum Modelling of Traffic Equilibrium Problem, in Giannessi, F. (ed.), Vector Variational Inequalities and Vector Equilibria, Kluwer Academic Publishers, Dordrecht, 97–111.

    Google Scholar 

  5. Gwinner, J. (1988), On continuum Modelling of Large Dense Networks in Urban Road Traffic, in Griffiths, J.D. (ed.), Mathematics in Transport Planning and Control IMA Conference, Cardiff.

  6. Maugeri, A. (1998), Dynamic Models and Generalized Equilibrium Problems, in: Giannessi, F. et al. (eds.), New Trends in Mathematical Programming, Kluwer Academic Publishers, Dordrecht, 191–202.

    Google Scholar 

  7. Maugeri, A. (1985), New Classes of Variational Inequalities and Applications to Equilibrium Problems, Methods of Operation Research 53, 129–131.

    Google Scholar 

  8. Maugeri, A. (1987), New Classes of Variational Inequalities and Applications to Equilibrium Problems, Rendiconti Accademia Nazionale delle Scienze deta dei XL 11, 224–285.

    Google Scholar 

  9. Maugeri, A. (2001), Equilibrium Problems and Variational Inequalities, in: Maugeri, A., Giannessi, F. and Pardalos, P. (eds.), Equilibrium Problems: Nonsmooth Optimization and Variational Inequalities Models, Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

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Authors and Affiliations

  1. D.I.M.E.T., Università di Reggio Calabria, Via Graziella, Loc. Feo di Vito, 89100, Reggio Calabria, Italy

    Giovanna Idone

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  1. Giovanna Idone
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Idone, G. Variational Inequalities and Applications to a Continuum Model of Transportation Network with Capacity Constraints. Journal of Global Optimization 28, 45–53 (2004). https://doi.org/10.1023/B:JOGO.0000006655.71863.53

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  • DOI: https://doi.org/10.1023/B:JOGO.0000006655.71863.53

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