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Weighted Quasi-Variational Inequalities in Non-pivot Hilbert Spaces and Applications

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  • Annamaria Barbagallo

    (University of Naples ‘Federico II’)

  • Stéphane Pia

    (University of Catania)

Abstract

The paper is devoted to the introduction of weighted quasi-variational inequalities in non-pivot Hilbert spaces. In the first part, we show some existence and regularity results for solutions to such weighted quasi-variational inequalities. The second part concerns the study of a new traffic equilibrium model, where weights and elastic demand occur. A weighted quasi-variational formulation for equilibrium conditions is provided. The general existence and regularity results obtained, in the first part, allow us to show the existence and the continuity of weighted elastic traffic equilibrium solutions. Finally, an example is provided.

Suggested Citation

  • Annamaria Barbagallo & Stéphane Pia, 2015. "Weighted Quasi-Variational Inequalities in Non-pivot Hilbert Spaces and Applications," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 781-803, March.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:3:d:10.1007_s10957-013-0497-z
    DOI: 10.1007/s10957-013-0497-z
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    References listed on IDEAS

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    1. Daniele, Patrizia, 2010. "Evolutionary variational inequalities and applications to complex dynamic multi-level models," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 46(6), pages 855-880, November.
    2. SALINETTI, Gabriella & WETS, Roger J.-B., 1979. "On the convergence of sequences of convex sets in finite dimensions," LIDAM Reprints CORE 352, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. 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.
    4. Annamaria Barbagallo & Stéphane Pia, 2011. "Weighted variational inequalities in non-pivot Hilbert spaces with applications," Computational Optimization and Applications, Springer, vol. 48(3), pages 487-514, April.
    5. Annamaria Barbagallo & Paolo Mauro, 2012. "Evolutionary Variational Formulation for Oligopolistic Market Equilibrium Problems with Production Excesses," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 288-314, October.
    6. A. Maugeri & F. Raciti, 2010. "Remarks on infinite dimensional duality," Journal of Global Optimization, Springer, vol. 46(4), pages 581-588, April.
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    Cited by:

    1. Annamaria Barbagallo & Paolo Mauro, 2016. "A General Quasi-variational Problem of Cournot-Nash Type and Its Inverse Formulation," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 476-492, August.

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