Jiménez, B.Novo, V.Vílchez, A.Huerga Pastor, Lidia2024-05-202024-05-202022-05-301029-494510.1080/02331934.2022.2081569https://hdl.handle.net/20.500.14468/12547We 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.enAtribución-NoComercial-SinDerivadas 4.0 Internacionalinfo:eu-repo/semantics/openAccessartículoScalarization in optimizationcontinuityvariable ordering structureoriented distancePainlevé–Kuratowski convergence