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Lipschitz behavior of solutions to nonconvex semi-infinite vector optimization problems

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  • N. Huy
  • D. Kim

Abstract

This paper is devoted to developing new applications from the limiting subdifferential in nonsmooth optimization and variational analysis to the study of the Lipschitz behavior of the Pareto solution maps in parametric nonconvex semi-infinite vector optimization problems (SIVO for brevity). We establish sufficient conditions for the Aubin Lipschitz-like property of the Pareto solution maps of SIVO under perturbations of both the objective function and constraints. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • N. Huy & D. Kim, 2013. "Lipschitz behavior of solutions to nonconvex semi-infinite vector optimization problems," Journal of Global Optimization, Springer, vol. 56(2), pages 431-448, June.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:2:p:431-448
    DOI: 10.1007/s10898-011-9829-4
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    References listed on IDEAS

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    1. Todorov, Maxim Ivanov, 1996. "Kuratowski convergence of the efficient sets in the parametric linear vector semi-infinite optimization," European Journal of Operational Research, Elsevier, vol. 94(3), pages 610-617, November.
    2. N. Q. Huy & J.-C. Yao, 2011. "Semi-Infinite Optimization under Convex Function Perturbations: Lipschitz Stability," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 237-256, February.
    3. N. D. Yen, 1997. "Stability of the Solution Set of Perturbed Nonsmooth Inequality Systems and Application," Journal of Optimization Theory and Applications, Springer, vol. 93(1), pages 199-225, April.
    4. M. J. Cánovas & A. Hantoute & M. A. López & J. Parra, 2008. "Stability of Indices in the KKT Conditions and Metric Regularity in Convex Semi-Infinite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 139(3), pages 485-500, December.
    5. T. Chuong & N. Huy & J. Yao, 2009. "Stability of semi-infinite vector optimization problems under functional perturbations," Computational Optimization and Applications, Springer, vol. 45(4), pages 583-595, December.
    6. Chuong, T.D. & Huy, N.Q. & Yao, J.C., 2010. "Pseudo-Lipschitz property of linear semi-infinite vector optimization problems," European Journal of Operational Research, Elsevier, vol. 200(3), pages 639-644, February.
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    Cited by:

    1. Thai Doan Chuong & Jen-Chih Yao, 2014. "Isolated and Proper Efficiencies in Semi-Infinite Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 447-462, August.

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