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.

Uderzo, A. (2023). Conditions for the stability of ideal efficient solutions in parametric vector optimization via set-valued inclusions. JOURNAL OF GLOBAL OPTIMIZATION, 85(4), 917-940 [10.1007/s10898-022-01232-1].

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

Uderzo A.
2023

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.
Articolo in rivista - Articolo scientifico
Calmness; Generalized derivatives; Ideal efficient solutions; Lipschitz lower semicontinuity; Vector optimization;
English
5-set-2022
2023
85
4
917
940
open
Uderzo, A. (2023). Conditions for the stability of ideal efficient solutions in parametric vector optimization via set-valued inclusions. JOURNAL OF GLOBAL OPTIMIZATION, 85(4), 917-940 [10.1007/s10898-022-01232-1].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/417398
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