On the Scalarization of Set-Valued Optimization Problems with Respect to Total Ordering Cones

Mahide Küçük (), Mustafa Soyertem () and Yalçin Küçük ()
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Mahide Küçük: Anadolu University
Mustafa Soyertem: Anadolu University
Yalçin Küçük: Anadolu University

A chapter in Operations Research Proceedings 2010, 2011, pp 347-352 from Springer

Abstract: Abstract A construction method of total ordering cone on n dimensional Euclidean space was given, it was shown that any total ordering cone is isomorphic to the lexicographic cone, also, existence of a total ordering cone that contain given cone with a compact base was shown and by using this cone, a solving method of vector and set-valued optimization problems was given recently by Küçük et.al. In this work, it is shown that the minimal element for the set-valued optimization problem with respect to the total ordering cone is also minimal element for the corresponding optimization problem. In addition, we give examples that show the absence of the relationships between the continuity of a set valued map and K-minimal element of this map.

Keywords: Partial Order; Construction Method; Vector Optimization; Minimal Element; Total Order (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:oprchp:978-3-642-20009-0_55

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DOI: 10.1007/978-3-642-20009-0_55

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