Approximate proper solutions in vector optimization with variable ordering structure
In this paper, we study approximate proper efficient (nondominated and minimal) solutions of vector optimization problems with variable ordering structures (VOSs). In vector optimization with VOS, the partial order-ing cone depends on the elements of the image set. Approximate proper efficient/nondo...
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| Format: | Article |
| Language: | English |
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Ferdowsi University of Mashhad
2024-01-01
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| Series: | Iranian Journal of Numerical Analysis and Optimization |
| Subjects: | |
| Online Access: | https://ijnao.um.ac.ir/article_44384_f351ec72f152873bde22180d5f736c21.pdf |
| _version_ | 1827342017945927680 |
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| author | S. Shahbeyk |
| author_facet | S. Shahbeyk |
| author_sort | S. Shahbeyk |
| collection | DOAJ |
| description | In this paper, we study approximate proper efficient (nondominated and minimal) solutions of vector optimization problems with variable ordering structures (VOSs). In vector optimization with VOS, the partial order-ing cone depends on the elements of the image set. Approximate proper efficient/nondominated/ minimal solutions are defined in different senses (Henig, Benson, and Borwein) for problems with VOSs from new stand-points. The relationships among the introduced notions are studied, and some scalarization approaches are developed to characterize these solutions. These scalarization results based on new functionals defined by elements from the dual cones are given. Moreover, some existing results are ad-dressed. |
| first_indexed | 2024-03-07T22:00:21Z |
| format | Article |
| id | doaj.art-b26144e0c6e8450ba004a96a8caaa768 |
| institution | Directory Open Access Journal |
| issn | 2423-6977 2423-6969 |
| language | English |
| last_indexed | 2024-03-07T22:00:21Z |
| publishDate | 2024-01-01 |
| publisher | Ferdowsi University of Mashhad |
| record_format | Article |
| series | Iranian Journal of Numerical Analysis and Optimization |
| spelling | doaj.art-b26144e0c6e8450ba004a96a8caaa7682024-02-24T05:13:08ZengFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69772423-69692024-01-0114Issue 110713510.22067/ijnao.2023.83112.128844384Approximate proper solutions in vector optimization with variable ordering structureS. Shahbeyk0Department of Mathematics, Faculty of Statistics, Mathematics, and Computer Science, Allameh Tabataba’i University , Tehran, Iran.In this paper, we study approximate proper efficient (nondominated and minimal) solutions of vector optimization problems with variable ordering structures (VOSs). In vector optimization with VOS, the partial order-ing cone depends on the elements of the image set. Approximate proper efficient/nondominated/ minimal solutions are defined in different senses (Henig, Benson, and Borwein) for problems with VOSs from new stand-points. The relationships among the introduced notions are studied, and some scalarization approaches are developed to characterize these solutions. These scalarization results based on new functionals defined by elements from the dual cones are given. Moreover, some existing results are ad-dressed.https://ijnao.um.ac.ir/article_44384_f351ec72f152873bde22180d5f736c21.pdfapproximate proper solutionsvariable ordering structurescalar-izationvector optimization |
| spellingShingle | S. Shahbeyk Approximate proper solutions in vector optimization with variable ordering structure Iranian Journal of Numerical Analysis and Optimization approximate proper solutions variable ordering structure scalar-ization vector optimization |
| title | Approximate proper solutions in vector optimization with variable ordering structure |
| title_full | Approximate proper solutions in vector optimization with variable ordering structure |
| title_fullStr | Approximate proper solutions in vector optimization with variable ordering structure |
| title_full_unstemmed | Approximate proper solutions in vector optimization with variable ordering structure |
| title_short | Approximate proper solutions in vector optimization with variable ordering structure |
| title_sort | approximate proper solutions in vector optimization with variable ordering structure |
| topic | approximate proper solutions variable ordering structure scalar-ization vector optimization |
| url | https://ijnao.um.ac.ir/article_44384_f351ec72f152873bde22180d5f736c21.pdf |
| work_keys_str_mv | AT sshahbeyk approximatepropersolutionsinvectoroptimizationwithvariableorderingstructure |