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On Convergence Results for Weak Efficiency in Vector Optimization Problems with Equilibrium Constraints

Author

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  • M. B. Lignola

    (Università di Napoli)

  • J. Morgan

    (Università di Napoli)

Abstract

In this note, we prove that the convergence results for vector optimization problems with equilibrium constraints presented in Wu and Cheng (J. Optim. Theory Appl. 125, 453–472, 2005) are not correct. Actually, we show that results of this type cannot be established at all. This is due to the possible lack, even under nice assumptions, of lower convergence of the solution map for equilibrium problems, already deeply investigated in Loridan and Morgan (Optimization 20, 819–836, 1989) and Lignola and Morgan (J. Optim. Theory Appl. 93, 575–596, 1997).

Suggested Citation

  • M. B. Lignola & J. Morgan, 2007. "On Convergence Results for Weak Efficiency in Vector Optimization Problems with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 133(1), pages 117-121, April.
    • Handle: RePEc:spr:joptap:v:133:y:2007:i:1:d:10.1007_s10957-007-9198-9
    DOI: 10.1007/s10957-007-9198-9
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    References listed on IDEAS

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    1. Y N Wu & T C E Cheng, 2005. "Convergence Results for Weak Efficiency in Vector Optimization Problems with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 453-472, May.
    2. M. B. Lignola & J. Morgan, 1997. "Stability of Regularized Bilevel Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 93(3), pages 575-596, June.
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    Cited by:

    1. M. Beatrice Lignola & Jacqueline Morgan, 2015. "MinSup Problems with Quasi-equilibrium Constraints and Viscosity Solutions," CSEF Working Papers 393, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    2. M. Lignola & Jacqueline Morgan, 2012. "Approximate values for mathematical programs with variational inequality constraints," Computational Optimization and Applications, Springer, vol. 53(2), pages 485-503, October.

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