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Levitin–Polyak Well-Posedness for Optimization Problems with Generalized Equilibrium Constraints

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  • G. Wang

    (Qufu Normal University)

  • X. X. Huang

    (Chongqing University)

Abstract

In this paper, we consider Levitin–Polyak well-posedness of parametric generalized equilibrium problems and optimization problems with generalized equilibrium constraints. Some criteria for these types of well-posedness are derived. In particular, under certain conditions, we show that generalized Levitin–Polyak well-posedness of a parametric generalized equilibrium problem is equivalent to the nonemptiness and compactness of its solution set. Finally, for an optimization problem with generalized equilibrium constraints, we also obtain that, under certain conditions, Levitin–Polyak well-posedness in the generalized sense is equivalent to the nonemptiness and compactness of its solution set.

Suggested Citation

  • G. Wang & X. X. Huang, 2012. "Levitin–Polyak Well-Posedness for Optimization Problems with Generalized Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 27-41, April.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:1:d:10.1007_s10957-011-9958-4
    DOI: 10.1007/s10957-011-9958-4
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    References listed on IDEAS

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    1. M. B. Lignola, 2006. "Well-Posedness and L-Well-Posedness for Quasivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 119-138, January.
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    Cited by:

    1. M. Darabi & J. Zafarani, 2015. "Tykhonov Well-Posedness for Quasi-Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 458-479, May.

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