Variational principles in set optimization with domination structures and application to changing jobs
Fiche du document
- handle: 10670/1.da9qej
- hal: hal-02497051
- doi: 10.23952/jano.1.2019.3.03
Ce document est lié à :
info:eu-repo/semantics/altIdentifier/doi/10.23952/jano.1.2019.3.03
Mots-clés
MSC: 49J53, 65K10, 90C26.Sujets proches
Point-to-set mappings Multi-valued mappings Maps, Set-valued Multivalued mappings Many-valued mappings Mappings, Point-to-set Professional services Jobs Careers Career patterns Jobs Careers Trades Career patternsCiter ce document
Truong Quang Bao et al., « Variational principles in set optimization with domination structures and application to changing jobs », HAL-SHS : économie et finance, ID : 10.23952/jano.1.2019.3.03
Métriques
Partage / Export
Résumé
This paper is devoted to new versions of Ekeland’s variational principle in set optimization with domination structure, where set optimization is an extension of vector optimization from vector-valued functions to set-valued maps using Kuroiwa’s set-less relations to compare one entire image set with another whole image set, and where domination structure is an extension of ordering cone in vector optimization; it assigns each element of the image space to its own domination set. We use Gerstewitz’s nonlinear scalarization function to convert a set-valued map into an extended real-valued function and the idea of the proof of Dancs-Hegedüs-Medvegyev’s fixed-point theorem. Our setting is applicable to dynamic processes of changing jobs in which the cost function does not satisfy the symmetry axiom of metrics and the class of set-valued maps acting from a quasimetric space into a real linear space. The obtained result is new even in simpler settings.