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dc.contributor.authorBagdasar, Ovidiu
dc.contributor.authorPopovici, Nicolae
dc.date.accessioned2018-04-24T13:32:25Z
dc.date.available2018-04-24T13:32:25Z
dc.date.issued2018-04-21
dc.identifier.citationBagdasar, O. and Popovici, N. (2018) 'Unifying local-global type properties in vector optimization.' Journal of Global Optimization, DOI: 10.1007/s10898-018-0656-8en
dc.identifier.doi10.1007/s10898-018-0656-8
dc.identifier.urihttp://hdl.handle.net/10545/622614
dc.description.abstractIt is well-known that all local minimum points of a semistrictly quasiconvex real-valued function are global minimum points. Also, any local maximum point of an explicitly quasiconvex real-valued function is a global minimum point, provided that it belongs to the intrinsic core of the function’s domain. The aim of this paper is to show that these “local min - global min” and “local max - global min” type properties can be extended and unified by a single general localglobal extremality principle for certain generalized convex vector-valued functions with respect to two proper subsets of the outcome space. For particular choices of these two sets, we recover and refine several local-global properties known in the literature, concerning unified vector optimization (where optimality is defined with respect to an arbitrary set, not necessarily a convex cone) and, in particular, classical vector/multicriteria optimization.
dc.description.sponsorshipNicolae Popovici’s research was supported by a grant of the Romanian Ministry of Research and Innovation, CNCS-UEFISCDI, project number PN-III-P4-ID-PCE- 2016-0190, within PNCDI III.en
dc.language.isoenen
dc.publisherSpringeren
dc.relation.urlhttps://rdcu.be/Ma7den
dc.subjectUnified vector optimizationen
dc.subjectAlgebraic local extremal pointen
dc.subjectTopological extremal pointen
dc.subjectGeneralized convexityen
dc.titleUnifying local-global type properties in vector optimization.en
dc.typeArticleen
dc.contributor.departmentUniversity of Derbyen
dc.identifier.journalJournal of Global Optimizationen
dc.date.accepted2018-04-16
html.description.abstractIt is well-known that all local minimum points of a semistrictly quasiconvex real-valued function are global minimum points. Also, any local maximum point of an explicitly quasiconvex real-valued function is a global minimum point, provided that it belongs to the intrinsic core of the function’s domain. The aim of this paper is to show that these “local min - global min” and “local max - global min” type properties can be extended and unified by a single general localglobal extremality principle for certain generalized convex vector-valued functions with respect to two proper subsets of the outcome space. For particular choices of these two sets, we recover and refine several local-global properties known in the literature, concerning unified vector optimization (where optimality is defined with respect to an arbitrary set, not necessarily a convex cone) and, in particular, classical vector/multicriteria optimization.


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