Characterizations of set relations with respect to variable domination structures via oriented distance function
Characterizations of set relations with respect to variable domination structures via oriented distance function
In this paper, we characterize several known set relations with respect to variable domination structures by defining scalarization functions in terms of the oriented distance function. The characterization of minimal elements of a family of sets and the properties of sets of minimal elements are discussed by means of scalarization functionals. An application of variable domination structures to uncertain vector optimization is also given.
49J53, 90C29, optimality conditions, Oriented distance function, set optimization, set relations, variable domination structures
1389-1407
Ansari, Qamrul Hasan
66737676-6bd6-41e7-b3b1-92216dddeb0b
Köbis, Elisabeth
072a94e2-75f7-405a-91c4-87e395101617
Sharma, Pradeep Kumar
142e7e4c-4dfa-4b91-9e7f-f2eda70380bf
2 September 2018
Ansari, Qamrul Hasan
66737676-6bd6-41e7-b3b1-92216dddeb0b
Köbis, Elisabeth
072a94e2-75f7-405a-91c4-87e395101617
Sharma, Pradeep Kumar
142e7e4c-4dfa-4b91-9e7f-f2eda70380bf
Ansari, Qamrul Hasan, Köbis, Elisabeth and Sharma, Pradeep Kumar
(2018)
Characterizations of set relations with respect to variable domination structures via oriented distance function.
Optimization, 67 (9), .
(doi:10.1080/02331934.2018.1493108).
Abstract
In this paper, we characterize several known set relations with respect to variable domination structures by defining scalarization functions in terms of the oriented distance function. The characterization of minimal elements of a family of sets and the properties of sets of minimal elements are discussed by means of scalarization functionals. An application of variable domination structures to uncertain vector optimization is also given.
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More information
Accepted/In Press date: 12 June 2018
e-pub ahead of print date: 9 July 2018
Published date: 2 September 2018
Additional Information:
Funding Information:
The first author was supported by DST-SERB [project number MTR/2017/000135].
Keywords:
49J53, 90C29, optimality conditions, Oriented distance function, set optimization, set relations, variable domination structures
Identifiers
Local EPrints ID: 485516
URI: http://eprints.soton.ac.uk/id/eprint/485516
ISSN: 0233-1934
PURE UUID: 4ccfefae-7aba-43f5-b71a-7bcce87cae95
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Date deposited: 07 Dec 2023 17:42
Last modified: 18 Mar 2024 04:17
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Contributors
Author:
Qamrul Hasan Ansari
Author:
Elisabeth Köbis
Author:
Pradeep Kumar Sharma
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