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Conditions for the stability of ideal efficient solutions in parametric vector optimization via set-valued inclusions

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  • Amos Uderzo

    (University of Milano-Bicocca)

Abstract

In present paper, an analysis of the stability behaviour of ideal efficient solutions to parametric vector optimization problems is conducted. A sufficient condition for the existence of ideal efficient solutions to locally perturbed problems and their nearness to a given reference value is provided by refining recent results on the stability theory of parameterized set-valued inclusions. More precisely, the Lipschitz lower semicontinuity property of the solution mapping is established, with an estimate of the related modulus. A notable consequence of this fact is the calmness behaviour of the ideal value mapping associated to the parametric class of vector optimization problems. Within such an analysis, a refinement of a recent existence result, specific for ideal efficient solutions to unperturbed problem and enhanced by related error bounds, is discussed. Some connections with the concept of robustness in multi-objective optimization are also sketched.

Suggested Citation

  • Amos Uderzo, 2023. "Conditions for the stability of ideal efficient solutions in parametric vector optimization via set-valued inclusions," Journal of Global Optimization, Springer, vol. 85(4), pages 917-940, April.
    • Handle: RePEc:spr:jglopt:v:85:y:2023:i:4:d:10.1007_s10898-022-01232-1
    DOI: 10.1007/s10898-022-01232-1
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    References listed on IDEAS

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    2. Stephen M. Robinson, 1991. "An Implicit-Function Theorem for a Class of Nonsmooth Functions," Mathematics of Operations Research, INFORMS, vol. 16(2), pages 292-309, May.
    3. 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.
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