Continuity of a scalarization in vector optimization with variable ordering structures and application to convergence of minimal solutions. (3rd April 2023)

• Record Type: Journal Article
• Authors: Huerga, L.; Jiménez, B.; Novo, V.; Vílchez, A.
• Is Part Of: Optimization. Volume 72:Number 4(2023)
• Page Start: 957
• Page End: 978
• Publication Date: 2023-04-03
• Subjects: Scalarization in optimization -- continuity -- variable ordering structure -- oriented distance -- Painlevé–Kuratowski convergence; 06A75 -- 49J53 -- 90C29 -- 49K40; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2022.2081569
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : 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.