A new scalarization approach and applications in set optimization

In this paper, we introduce a new nonlinear scalarization function and apply it to investigate optimality conditions and scalar representations for minimal sets and set optimization problems with the set less order relation. First, we propose a new scalarization function for sets belonging to the po...

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Published in:	Optimization Vol. 72; no. 4; pp. 1093 - 1117
Main Authors:	Anh, Lam Quoc, Thanh Duoc, Pham, Thi Thuy Duong, Tran
Format:	Journal Article
Language:	English
Published:	Philadelphia Taylor & Francis 03-04-2023 Taylor & Francis LLC
Subjects:	nonlinear scalarization optimality condition Optimization Representations scalar representation set less order relation Set optimization problem
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Abstract	In this paper, we introduce a new nonlinear scalarization function and apply it to investigate optimality conditions and scalar representations for minimal sets and set optimization problems with the set less order relation. First, we propose a new scalarization function for sets belonging to the power set of a normed space and discuss its properties. Next, we apply such properties to formulate sufficient and necessary optimality conditions for strictly minimal and weakly minimal sets. Finally, under suitable adjustments, we provide nonlinear scalarization functions and investigate scalar representations of strictly efficient solution and weakly efficient solution sets of the reference problems.
AbstractList	In this paper, we introduce a new nonlinear scalarization function and apply it to investigate optimality conditions and scalar representations for minimal sets and set optimization problems with the set less order relation. First, we propose a new scalarization function for sets belonging to the power set of a normed space and discuss its properties. Next, we apply such properties to formulate sufficient and necessary optimality conditions for strictly minimal and weakly minimal sets. Finally, under suitable adjustments, we provide nonlinear scalarization functions and investigate scalar representations of strictly efficient solution and weakly efficient solution sets of the reference problems.
Author	Anh, Lam Quoc Thi Thuy Duong, Tran Thanh Duoc, Pham
Author_xml	– sequence: 1 givenname: Lam Quoc surname: Anh fullname: Anh, Lam Quoc email: quocanh@ctu.edu.vn organization: Can Tho University – sequence: 2 givenname: Pham surname: Thanh Duoc fullname: Thanh Duoc, Pham organization: University of Science, Vietnam National University – sequence: 3 givenname: Tran surname: Thi Thuy Duong fullname: Thi Thuy Duong, Tran organization: Can Tho University
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Cites_doi	10.1007/s00186-019-00676-8 10.1016/j.orl.2019.03.005 10.1016/j.na.2006.08.013 10.1287/moor.4.1.79 10.1007/s10957-020-01657-2 10.1007/s10898-014-0179-x 10.1007/BF01457934 10.1007/s10957-010-9752-8 10.1007/s10898-018-0712-4 10.1007/s40314-021-01458-x 10.1023/A:1016031214488 10.1080/00036811.2015.1109079 10.1080/02331934.2019.1602771 10.1007/BF00940478 10.1007/978-3-642-50280-4 10.1016/j.na.2012.02.004 10.1016/j.jmaa.2006.01.033 10.1080/02331934.2017.1322082 10.1080/02331934.2016.1219355 10.1007/s00186-019-00679-5 10.1007/s00186-020-00736-4 10.1007/s40306-020-00370-6 10.1016/j.orl.2020.10.002 10.1080/02331934.2019.1598406 10.1007/978-3-662-48670-2_2
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Title	A new scalarization approach and applications in set optimization
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