Unifying local-global type properties in vector optimization.
|Authors||Bagdasar, Ovidiu and Popovici, Nicolae|
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|
|Journal||Journal of Global Optimization|
|Digital Object Identifier (DOI)||https://doi.org/10.1007/s10898-018-0656-8|
|Web address (URL)||http://hdl.handle.net/10545/622614|
|Publication dates||21 Apr 2018|
|Publication process dates|
|Deposited||24 Apr 2018, 13:32|
|Accepted||16 Apr 2018|
|Contributors||University of Derby|
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