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Optimization in Science and Engineering pp 89–96Cite as

General Traffic Equilibrium Problem with Uncertainty and Random Variational Inequalities

Abstract

In the paper we study, in a Hilbert space setting, a general random traffic equilibrium problem. For this problem we give a random generalized Wardrop equilibrium condition and we characterize an equilibrium distribution by means of a variational inequality. Finally some existence results are provided.

Keywords

  • Traffic Network Problems
  • Random Variational Inequalities
  • Hilbert Space Setting
  • Path Flow Vector
  • Generalized Complementarity Problem

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  • DOI: 10.1007/978-1-4939-0808-0_4
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References

  1. Brezis, H.: Équations et inéquations non linéaires dans les espaces vectoriels en dualité. Annales de l’Institut Fourier 18, 115–175 (1968)

    CrossRef  MATH  MathSciNet  Google Scholar 

  2. Daniele, P., Maugeri, A., Oettli, W.: Time-dependent traffic equilibria. J. Optim. Theory Appl. 103(3), 543–555 (1999)

    CrossRef  MATH  MathSciNet  Google Scholar 

  3. Evstigneev, I.V., Taksar, M.I.: Equilibrium states of random economies with locally interacting agents and solutions to stochastic variational inequalities in \(\langle L_{1},L_{\infty }\rangle\). Ann. Oper. Res. 114, 145–165(2002)

    CrossRef  MATH  MathSciNet  Google Scholar 

  4. Ganguly, A., Wadhwa, K.: On random variational inequalities. J. Math. Anal. Appl. 206, 315–321 (1997)

    CrossRef  MATH  MathSciNet  Google Scholar 

  5. Gwinner, J., Raciti, F.: On a class of random variational inequalities on random sets. Numer. Funct. Anal. Optim. 27(56), 619-636 (2006)

    CrossRef  MATH  MathSciNet  Google Scholar 

  6. Gwinner, J., Raciti, F.: Random equilibrium problems on networks. Math. Comput. Model. 43(7–8), 880–891 (2006)

    CrossRef  MATH  MathSciNet  Google Scholar 

  7. Gwinner, J., Raciti, F.: Some equilibrium problems under uncertainty and random variational inequalities. Ann. Oper. Res. 200(1), 299–319 (2012)

    CrossRef  MATH  MathSciNet  Google Scholar 

  8. Gürkan, G., Özge, A.Y., Robinson, S.M.: Sample-path solution of stochastic variational inequalities. Math. Program. 84, 313–333 (1999)

    CrossRef  MATH  MathSciNet  Google Scholar 

  9. Maugeri, A., Raciti, F.: On general infinite dimensional complementarity problems. Optim. Lett. 2, 71–90 (2008)

    CrossRef  MATH  MathSciNet  Google Scholar 

  10. Maugeri, A., Raciti, F.: On existence theorems for monotone and nonmonotone variational inequalities. J. Convex Anal. 16, 899–911 (2009)

    MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Catania, Viale A. Doria, 6, 95125, Catania, Italy

    Patrizia Daniele & Antonino Maugeri

  2. D.I.I.E.S., “Mediterranea” University of Reggio Calabria, 89060, Reggio Calabria, Italy

    Sofia Giuffrè

Authors
  1. Patrizia Daniele
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  2. Sofia Giuffrè
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  3. Antonino Maugeri
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Corresponding author

Correspondence to Patrizia Daniele .

Editor information

Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Princeton University Dept. Chemical Engineering, Princeton, New Jersey, USA

    Christodoulos A. Floudas

  3. Dept. Industrial & Systems Engineering, Texas A&M University, College Station, Texas, USA

    Sergiy Butenko

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Daniele, P., Giuffrè, S., Maugeri, A. (2014). General Traffic Equilibrium Problem with Uncertainty and Random Variational Inequalities. In: Rassias, T., Floudas, C., Butenko, S. (eds) Optimization in Science and Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0808-0_4

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