Variational Inequalities Characterizing Weak Minimality in Set Optimization

Variational Inequalities Characterizing Weak Minimality in Set Optimization

We introduce the notion of weak minimizer in set optimization. Necessary and sufficient conditions in terms of scalarized variational inequalities of Stampacchia and Minty type, respectively, are proved. As an application, we obtain necessary and sufficient optimality conditions for weak efficiency...

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Veröffentlicht in:Journal of optimization theory and applications 2015-09, Vol.166 (3), p.804-824
Hauptverfasser: Crespi, Giovanni P., Rocca, Matteo, Schrage, Carola
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Engineering
Inequalities
Inequality
Mathematical analysis
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Set theory
Studies
Theory of Computation
Variational principles
Vectors (mathematics)
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Beschreibung
Zusammenfassung:We introduce the notion of weak minimizer in set optimization. Necessary and sufficient conditions in terms of scalarized variational inequalities of Stampacchia and Minty type, respectively, are proved. As an application, we obtain necessary and sufficient optimality conditions for weak efficiency of vector optimization in infinite-dimensional spaces. A Minty variational principle in this framework is proved as a corollary of our main result.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-014-0679-3