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Unifying local-global type properties in vector optimization.
- Source :
- Journal of Global Optimization; Oct2018, Vol. 72 Issue 2, p155-179, 25p
- Publication Year :
- 2018
-
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 local-global 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09255001
- Volume :
- 72
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Journal of Global Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 131705364
- Full Text :
- https://doi.org/10.1007/s10898-018-0656-8