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arXiv · 2111.00461

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

Amos Uderzo
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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 is also discussed.

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Amos Uderzo. 2021-10-31. A condition for the stability of ideal efficient solutions in parametric vector optimization via set-valued inclusions. https://arxiv.org/abs/2111.00461

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