On the sensitivity of Pareto efficiency in set-valued optimization problems

Marius Durea () and Radu Strugariu ()
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Marius Durea: “Alexandru Ioan Cuza” University
Radu Strugariu: “Gheorghe Asachi” Technical University

Journal of Global Optimization, 2020, vol. 78, issue 3, No 8, 596 pages

Abstract: Abstract In this paper we present two main situations when the limit of Pareto minima of a sequence of perturbations of a set-valued map F is a critical point of F. The concept of criticality is understood in the Fermat generalized sense by means of limiting (Mordukhovich) coderivative. Firstly, we consider perturbations of enlargement type which, in particular, cover the case of perturbation with dilating cones. Secondly, we present the case of Aubin type perturbations, and for this we introduce and study a new concept of openness with respect to a cone.

Keywords: Pareto minimality; Sensitivity; Criticality; Openness with respect to a cone; 49J53; 90C29; 49K40 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10898-020-00925-9

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