Journal of Global Optimization

, Volume 40, Issue 1–3, pp 175–184 | Cite as

Hölder continuity of solutions to elastic traffic network models

  • Mohamed Ait MansourEmail author
  • Laura Scrimali


This paper aims to study stability and sensitivity analysis for quasi-variational inequalities which model traffic network equilibrium problems with elastic travel demand. In particular, we provide a Hölder stability result under parametric perturbations.


Quasi-variational inequalities Hölder continuity Traffic equilibrium problem 


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  1. 1.
    Adly S., Ait Mansour M. and Scrimali L. (2005). Sensitivity analysis of solutions to a class of quasi-variational inequalities. Bollettino dell’Unione Matematica Italiana, Sezione B 8(8): 767–771 Google Scholar
  2. 2.
    Ait Mansour M. and Riahi H. (2005). Sensitivity analysis for abstract equilibrium problems. J. Math. Anal. Appl. 306: 684–691 CrossRefGoogle Scholar
  3. 3.
    Aubin J.-P. (1984). Lipschitz behavior of solutions to convex minimization problems. Math. Oper. Res. 9: 87–111 Google Scholar
  4. 4.
    Baiocchi F. and Capelo A. (1984). Variational and Quasivariational Inequalities. Application to Free Boundary Problems. Wiley, New York Google Scholar
  5. 5.
    Chang D. and Pang J.-S. (1982). The generalized quasi-variational inequality problem. Math. Oper. Res. 7: 211–222 CrossRefGoogle Scholar
  6. 6.
    Cubiotti P. (1997). Generalized quasi-variational inequalities in infininite dimensional spaces. J. Optim. Theory Appl. 92: 457–475 CrossRefGoogle Scholar
  7. 7.
    De Luca M. and Maugeri A. (1989). Quasi-variational inequality and applications to equilibrium problems with elastic demands. In: Clarke, F.M., Dem’yanov, V.F. and Giannessi, F. (eds) Non smooth Optimization and Related Topics, vol. 43., pp 61–77. Plenum Press, New York Google Scholar
  8. 8.
    De Luca M. (1997). Existence of solutions for a time-dependent quasi-variational inequality. Supplemento Rend. Circ. Mat. Palermo Serie 2(48): 101–106 Google Scholar
  9. 9.
    Fiacco A.V. and McCormick G.P. (1984). Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Wiley, New York Google Scholar
  10. 10.
    Fiacco A.V. (1976). Sensitivity analysis for nonlinear programming using penality methods. Math. progam. 10: 287–311 CrossRefGoogle Scholar
  11. 11.
    Fiacco A.V. (1983). An Introduction to Sensitivity and Stability Analysis in Nonlinear Programming. Academic, New York Google Scholar
  12. 12.
    Kyparisis J. (1987). Sensitivity analysis framework for variational inequalities. Math. Program. 38: 203–213 CrossRefGoogle Scholar
  13. 13.
    Mordukhovich B. (2006). Variational Analysis and Generalized Differentiation. Springer, New York Google Scholar
  14. 14.
    Robinson S.M. (1979). Generalized equations and their solutions, Part I: basic theory. Math. Program. Study 10: 128–141 Google Scholar
  15. 15.
    Robinson S.M. (1980). Strongly regular generalized equations. Math. Oper. Res. 10: 43–62 Google Scholar
  16. 16.
    Scrimali L. (2004). Quasi-variational inequalities in transportation networks. Math. Models Methods Appl. Sci. 14(10): 1541–1560 CrossRefGoogle Scholar
  17. 17.
    Shapiro A. (1985). Second order sensitivity analysis and asymptotic theory of parametrized nonlinear onlinear programs. Math. Program. 33: 280–299 CrossRefGoogle Scholar
  18. 18.
    Shapiro A. (2005). Sensitivity analysis of parameterized variational inequalities. Math. Oper. Res. 30: 109–126 CrossRefGoogle Scholar
  19. 19.
    Smith M.J. (1979). The existence, uniqueness and stability of traffic equilibrium. Transport. Res. 138: 295–304 CrossRefGoogle Scholar
  20. 20.
    Walkup D.W. and Wets R.J-B. (1969). A Lipschitzian of convex polyhedral. Proc. Am. Math. Soc. 23: 167–178 CrossRefGoogle Scholar
  21. 21.
    Wardrop J.G.: Some theoretical aspects of road traffic research. Proc. Inst. Civil Eng. Part II 325–378 (1952)Google Scholar
  22. 22.
    Yen N.D. (1995). Hölder continuity of solutions to a parametric variational inequality. Appl. Math. Optim. 31: 245–255 CrossRefGoogle Scholar

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© Springer Science+Business Media LLC 2007

Authors and Affiliations

  1. 1.Département  de  MathématiquesUniversité de PerpignanPerpignanFrance
  2. 2.Dipartimento di Matematica e InformaticaUniversità di CataniaCataniaItaly

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