Unifying local-global type properties in vector optimization.
Journal article
Authors | Bagdasar, Ovidiu and Popovici, Nicolae |
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Abstract | It 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. |
It is well-known that all local minimum points of a semistrictly quasiconvex | |
Keywords | Unified vector optimization; Algebraic local extremal point; Topological extremal point; Generalized convexity |
Year | 2018 |
Journal | Journal of Global Optimization |
Publisher | Springer |
Digital Object Identifier (DOI) | https://doi.org/10.1007/s10898-018-0656-8 |
Web address (URL) | http://hdl.handle.net/10545/622614 |
hdl:10545/622614 | |
Publication dates | 21 Apr 2018 |
Publication process dates | |
Deposited | 24 Apr 2018, 13:32 |
Accepted | 16 Apr 2018 |
Contributors | University of Derby |
File | |
File | File Access Level Open |
https://repository.derby.ac.uk/item/937zq/unifying-local-global-type-properties-in-vector-optimization
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