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

Amos Uderzo ()
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Amos Uderzo: University of Milano-Bicocca

Journal of Global Optimization, 2023, vol. 85, issue 4, No 6, 917-940

Abstract: 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.

Keywords: Ideal efficient solutions; Vector optimization; Lipschitz lower semicontinuity; Calmness; Generalized derivatives; 90C31; 90C29; 49J53; 49J52 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01232-1

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