Calmness of efficient solution maps in parametric vector optimization

The paper is concerned with the stability theory of the efficient solution map of a parametric vector optimization problem. Utilizing the advanced tools of modern variational analysis and generalized differentiation, we study the calmness of the efficient solution map. More explicitly, new sufficien...

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Bibliographic Details
Published inJournal of global optimization Vol. 51; no. 4; pp. 677 - 688
Main Authors Chuong, T. D., Kruger, A. Y., Yao, J.-C.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.12.2011
Springer Nature B.V
Subjects
Banach spaces
Computer Science
Mapping
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Studies
90C31
49K40
49J52
Coderivative
Efficient solution map
Implicit multifunction
90C29
Calmness
Parametric vector optimization
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Summary:The paper is concerned with the stability theory of the efficient solution map of a parametric vector optimization problem. Utilizing the advanced tools of modern variational analysis and generalized differentiation, we study the calmness of the efficient solution map. More explicitly, new sufficient conditions in terms of the Fréchet and limiting coderivatives of parametric multifunctions for this efficient solution map to have the calmness at a given point in its graph are established by employing the approach of implicit multifunctions. Examples are also provided for analyzing and illustrating the results obtained.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-011-9651-z