Stability of semi-infinite vector optimization problems under functional perturbations

This paper is devoted to the study of continuity properties of Pareto solution maps for parametric semi-infinite vector optimization problems (PSVO). We establish new necessary conditions for lower and upper semicontinuity of Pareto solution maps under functional perturbations of both objective func...

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Published inJournal of global optimization Vol. 45; no. 4; pp. 583 - 595
Main Authors Chuong, T. D., Huy, N. Q., Yao, J. C.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.12.2009
Springer Nature B.V
Subjects
Applied mathematics
Computer Science
Hierarchies
Mapping
Mathematical problems
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Studies
90C31
Pareto solution map
Upper semicontinuity
Lower semicontinuity
Stability
Semi-infinite vector optimization
49K40
90C29
46N10
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ISSN0925-5001
1573-2916
DOI10.1007/s10898-008-9391-x

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Summary:This paper is devoted to the study of continuity properties of Pareto solution maps for parametric semi-infinite vector optimization problems (PSVO). We establish new necessary conditions for lower and upper semicontinuity of Pareto solution maps under functional perturbations of both objective functions and constraint sets. We also show that the necessary condition becomes sufficient for the lower and upper semicontinuous properties in the special case where the constraint set mapping is lower semicontinuous at the reference point. Examples are given to illustrate the obtained results.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-008-9391-x