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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| Published in: | Journal of global optimization Vol. 78; no. 3; pp. 581 - 596 |
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| Language: | English |
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01.11.2020
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| 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. |
|---|---|
| AbstractList | 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. 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. |
| Audience | Academic |
| Author | Durea, Marius Strugariu, Radu |
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| CitedBy_id | crossref_primary_10_1016_j_icheatmasstransfer_2021_105867 |
| Cites_doi | 10.1007/s10898-019-00761-6 10.1007/s10107-008-0249-2 10.1007/s10957-016-0986-y 10.1007/BF00935007 10.1090/S0002-9939-2010-10490-2 10.1080/02331934.2011.587189 10.1016/j.na.2011.02.019 10.1007/s10898-012-9910-7 10.1007/978-3-319-64277-2 10.1007/s11117-016-0412-6 10.1137/140980612 10.1137/11082470X 10.1016/j.jmaa.2006.12.009 10.1080/02331930903531527 10.1007/s10898-017-0505-1 10.1006/jmaa.1995.5054 10.1016/j.jmaa.2018.12.071 10.1016/j.jmaa.2008.07.039 10.1007/978-3-319-92775-6 10.1080/02331934.2019.1613403 10.1007/978-1-4939-1037-3 |
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| DOI | 10.1007/s10898-020-00925-9 |
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| Keywords | Pareto minimality Sensitivity 49J53 49K40 Openness with respect to a cone 90C29 Criticality |
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| Snippet | 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
.... 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... |
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| SubjectTerms | Analysis Computer Science Cones Critical point Efficiency Mapping Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Pareto efficiency Pareto optimum Perturbation Real Functions |
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| Title | On the sensitivity of Pareto efficiency in set-valued optimization problems |
| URI | https://link.springer.com/article/10.1007/s10898-020-00925-9 https://www.proquest.com/docview/2608627503 |
| Volume | 78 |
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