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.

Variational Inequalities Characterizing Weak Minimality in Set Optimization

CRESPI, GIOVANNI PAOLO;ROCCA, MATTEO;
2015-01-01

Abstract

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.
2015
Scalarization; Set optimization; Variational inequalities; Weak efficiency;
Crespi, GIOVANNI PAOLO; Rocca, Matteo; Schrage, Carola
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/1976124
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