Crespi Giovanni P. () (Facoltà di Scienze Economiche Aosta, Italy) Ginchev Ivan () (Department of Mathematics Varna, Bulgaria) Rocca Matteo () (Department of Economics, University of Insubria, Italy)
Abstract
A constrained optimization problem with set-valued data is considered. Different kind of solutions are defined for such a problem. We recall weak minimizer, efficient minimizer and proper minimizer. The latter are defined in a way that embrace also the case when the ordering cone is not pointed. Moreover we present the new concept of isolated minimizer for set-valued optimization. These notions are investigated and appear when establishing first-order necessary and sufficient optimality conditions derived in terms of a Dini type derivative for set-valued maps. The case of convex (along rays) data is considered when studying sufficient optimality conditions for weak minimizers. Key words: Vector optimization, Set-valued optimization, First-order optimality conditions.
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