Variational inequalities characterizing weak minimality in set optimization
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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.
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Crespi GP; Schrage C (Springer, 2015)We study necessary and sufficient conditions to attain solutions of set-optimization problems in terms of variational inequalities of Stampacchia and Minty type. The notion of solution we deal with has been introduced by ...
Weak minimizers, minimizers and variational inequalities for set-valued functions: A blooming wreath? Crespi GP; Schrage C (2016)Recently, necessary and sufficient conditions in terms of variational inequalities have been introduced to characterize minimizers of convex setvalued functions. Similar results have been proved for a weaker concept of ...
Crespi GP; Hamel AH; Schrage C (Elsevier, 2015)Extremal problems are studied involving an objective function with values in (order) complete lattices of sets generated by so called set relations. Contrary to the popular paradigm in vector optimization, the solution ...