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Lipschitz Continuity Results for a Class of Variational Inequalities and Applications: A Geometric Approach

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  • A. Causa

    (Università di Catania)

  • F. Raciti

    (Università di Catania)

Abstract

We consider a class of parametric variational inequalities which, under suitable assumptions, admit an equivalent integral formulation. We study the Lipschitz continuity of the solution and treat in detail the case in which the parametric constraint set is a polytope. Finally, the results obtained are applied to the time-dependent traffic equilibrium problem.

Suggested Citation

  • A. Causa & F. Raciti, 2010. "Lipschitz Continuity Results for a Class of Variational Inequalities and Applications: A Geometric Approach," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 235-248, May.
    • Handle: RePEc:spr:joptap:v:145:y:2010:i:2:d:10.1007_s10957-009-9622-4
    DOI: 10.1007/s10957-009-9622-4
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    References listed on IDEAS

    as
    1. Shu Lu, 2008. "Sensitivity of Static Traffic User Equilibria with Perturbations in Arc Cost Function and Travel Demand," Transportation Science, INFORMS, vol. 42(1), pages 105-123, February.
    2. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
    3. Smith, M. J., 1979. "The existence, uniqueness and stability of traffic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 295-304, December.
    4. F. Raciti & P. Falsaperla, 2007. "Improved Noniterative Algorithm for Solving the Traffic Equilibrium Problem," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 401-411, June.
    5. P. Daniele & A. Maugeri & W. Oettli, 1999. "Time-Dependent Traffic Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 103(3), pages 543-555, December.
    6. Shu Lu & Stephen M. Robinson, 2008. "Variational Inequalities over Perturbed Polyhedral Convex Sets," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 689-711, August.
    7. N. D. Yen, 1995. "Lipschitz Continuity of Solutions of Variational Inequalities with a Parametric Polyhedral Constraint," Mathematics of Operations Research, INFORMS, vol. 20(3), pages 695-708, August.
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    Cited by:

    1. A. Causa & F. Raciti, 2013. "A Purely Geometric Approach to the Problem of Computing the Projection of a Point on a Simplex," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 524-528, February.

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