A condition for the stability of ideal efficient solutions in parametric vector optimization via set-valued inclusions
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.
Cite
@article{arxiv.2111.00461,
title = {A condition for the stability of ideal efficient solutions in parametric vector optimization via set-valued inclusions},
author = {Amos Uderzo},
journal= {arXiv preprint arXiv:2111.00461},
year = {2021}
}