E-invexity and generalized E-invexity in E-differentiable multiobjective programming
In this paper, a new concept of generalized convexity is introduced for not necessarily differentiable vector optimization problems. For an E-differentiable function, the concept of E-invexity is introduced as a generalization of the E-differentiable E-convexity notion. In addition, some properties of...
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| Format: | Article |
| Language: | English |
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EDP Sciences
2019-01-01
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| Series: | ITM Web of Conferences |
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| Online Access: | https://www.itm-conferences.org/articles/itmconf/pdf/2019/01/itmconf_amcse18_01002.pdf |
| _version_ | 1818664201356312576 |
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| author | Abdulaleem Najeeb |
| author_facet | Abdulaleem Najeeb |
| author_sort | Abdulaleem Najeeb |
| collection | DOAJ |
| description | In this paper, a new concept of generalized convexity is introduced for not necessarily differentiable vector optimization problems. For an E-differentiable function, the concept of E-invexity is introduced as a generalization of the E-differentiable E-convexity notion. In addition, some properties of E-differentiable E-invex functions are investigated. Furthermore, the so-called E-Karush-Kuhn-Tucker necessary optimality conditions are established for the considered E-differentiable vector optimization problems with both inequality and equality constraints. Also, the sufficiency of the E-Karush-Kuhn-Tucker necessary optimality conditions are proved for such E-differentiable vector optimization problems in which the involved functions are E-invex and/or generalized E-invex. |
| first_indexed | 2024-12-17T05:28:58Z |
| format | Article |
| id | doaj.art-060060a7b04944aeb0c1a12a7cd871d3 |
| institution | Directory Open Access Journal |
| issn | 2271-2097 |
| language | English |
| last_indexed | 2024-12-17T05:28:58Z |
| publishDate | 2019-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ITM Web of Conferences |
| spelling | doaj.art-060060a7b04944aeb0c1a12a7cd871d32022-12-21T22:01:47ZengEDP SciencesITM Web of Conferences2271-20972019-01-01240100210.1051/itmconf/20192401002itmconf_amcse18_01002E-invexity and generalized E-invexity in E-differentiable multiobjective programmingAbdulaleem Najeeb0Department of Mathematics, Hadhramout UniversityIn this paper, a new concept of generalized convexity is introduced for not necessarily differentiable vector optimization problems. For an E-differentiable function, the concept of E-invexity is introduced as a generalization of the E-differentiable E-convexity notion. In addition, some properties of E-differentiable E-invex functions are investigated. Furthermore, the so-called E-Karush-Kuhn-Tucker necessary optimality conditions are established for the considered E-differentiable vector optimization problems with both inequality and equality constraints. Also, the sufficiency of the E-Karush-Kuhn-Tucker necessary optimality conditions are proved for such E-differentiable vector optimization problems in which the involved functions are E-invex and/or generalized E-invex.https://www.itm-conferences.org/articles/itmconf/pdf/2019/01/itmconf_amcse18_01002.pdfE-invex setE-invex functionE-differentiable functionE-Karush-Kuhn-Tucker necessary optimality conditions |
| spellingShingle | Abdulaleem Najeeb E-invexity and generalized E-invexity in E-differentiable multiobjective programming ITM Web of Conferences E-invex set E-invex function E-differentiable function E-Karush-Kuhn-Tucker necessary optimality conditions |
| title | E-invexity and generalized E-invexity in E-differentiable multiobjective programming |
| title_full | E-invexity and generalized E-invexity in E-differentiable multiobjective programming |
| title_fullStr | E-invexity and generalized E-invexity in E-differentiable multiobjective programming |
| title_full_unstemmed | E-invexity and generalized E-invexity in E-differentiable multiobjective programming |
| title_short | E-invexity and generalized E-invexity in E-differentiable multiobjective programming |
| title_sort | e invexity and generalized e invexity in e differentiable multiobjective programming |
| topic | E-invex set E-invex function E-differentiable function E-Karush-Kuhn-Tucker necessary optimality conditions |
| url | https://www.itm-conferences.org/articles/itmconf/pdf/2019/01/itmconf_amcse18_01002.pdf |
| work_keys_str_mv | AT abdulaleemnajeeb einvexityandgeneralizedeinvexityinedifferentiablemultiobjectiveprogramming |