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

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...

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Bibliographic Details
Published in:Journal of global optimization Vol. 78; no. 3; pp. 581 - 596
Main Authors: Durea, Marius, Strugariu, Radu
Format: Journal Article
Language:English
Published: New York Springer US 01.11.2020
Springer
Springer Nature B.V
Subjects:
Analysis
Computer Science
Cones
Critical point
Efficiency
Mapping
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Pareto efficiency
Pareto optimum
Perturbation
Real Functions
Pareto minimality
Sensitivity
49J53
49K40
Openness with respect to a cone
90C29
Criticality
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary: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.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-020-00925-9