Publicación: Continuity of a scalarization in vector optimization with variable ordering structures and application to convergence of minimal solutions
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2022-05-30
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Atribución-NoComercial-SinDerivadas 4.0 Internacional
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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Taylor & Francis
Resumen
We consider a scalarization function, which was introduced by Eichfelder [Variable ordering structures in vector optimization. Berlin: Springer-Verlag; 2014 (Series in vector optimization)], based on the oriented distance of Hiriart–Urruty with respect to a general variable ordering structure (VOS). We first study the continuity of the composition of a set-valued map with the oriented distance. Then, using the obtained results, we study the continuity of the scalarization function by extending some concepts of continuity for cone-valued maps. As an application, convergence in the sense of Painlevé–Kuratowski of sets of weak minimal solutions is provided, with the vector criterion and a VOS. Illustrative examples are also given.
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Categorías UNESCO
Palabras clave
Scalarization in optimization, continuity, variable ordering structure, oriented distance, Painlevé–Kuratowski convergence
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Centro
E.T.S. de Ingenieros Industriales
Departamento
Matemática Aplicada I