Approximate Subdifferential of the Difference of Two Vector Convex Mappings
This paper deals with the strong approximate subdifferential formula for the difference of two vector convex mappings in terms of the star difference. This formula is obtained via a scalarization process by using the approximate subdifferential of the difference of two real convex functions establis...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/12/2718 |
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| author | Abdelghali Ammar Mohamed Laghdir Ahmed Ed-dahdah Mohamed Hanine |
| author_facet | Abdelghali Ammar Mohamed Laghdir Ahmed Ed-dahdah Mohamed Hanine |
| author_sort | Abdelghali Ammar |
| collection | DOAJ |
| description | This paper deals with the strong approximate subdifferential formula for the difference of two vector convex mappings in terms of the star difference. This formula is obtained via a scalarization process by using the approximate subdifferential of the difference of two real convex functions established by Martinez-Legaz and Seeger, and the concept of regular subdifferentiability. This formula allows us to establish approximate optimality conditions characterizing the approximate strong efficient solution for a general DC problem and for a multiobjective fractional programming problem. |
| first_indexed | 2024-03-11T02:11:05Z |
| format | Article |
| id | doaj.art-26e62655804c4ed99d0d283ab4f6b69a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T02:11:05Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-26e62655804c4ed99d0d283ab4f6b69a2023-11-18T11:28:48ZengMDPI AGMathematics2227-73902023-06-011112271810.3390/math11122718Approximate Subdifferential of the Difference of Two Vector Convex MappingsAbdelghali Ammar0Mohamed Laghdir1Ahmed Ed-dahdah2Mohamed Hanine3Department of Computer Engineering, Networks and Telecommunications, National School of Applied Sciences, Cadi Ayyad University, BP. 63, Safi 46000, MoroccoDepartment of Mathematics, Faculty of Sciences, Chouaib Doukkali University, BP. 20, El Jadida 24000, MoroccoDepartment of Mathematics, Faculty of Sciences, Chouaib Doukkali University, BP. 20, El Jadida 24000, MoroccoDepartment of Telecommunications, Networks, and Informatics, National School of Applied Sciences, Chouaib Doukkali University, El Jadida 24000, MoroccoThis paper deals with the strong approximate subdifferential formula for the difference of two vector convex mappings in terms of the star difference. This formula is obtained via a scalarization process by using the approximate subdifferential of the difference of two real convex functions established by Martinez-Legaz and Seeger, and the concept of regular subdifferentiability. This formula allows us to establish approximate optimality conditions characterizing the approximate strong efficient solution for a general DC problem and for a multiobjective fractional programming problem.https://www.mdpi.com/2227-7390/11/12/2718vector optimizationoptimality conditionapproximate subdifferentialDC programming |
| spellingShingle | Abdelghali Ammar Mohamed Laghdir Ahmed Ed-dahdah Mohamed Hanine Approximate Subdifferential of the Difference of Two Vector Convex Mappings Mathematics vector optimization optimality condition approximate subdifferential DC programming |
| title | Approximate Subdifferential of the Difference of Two Vector Convex Mappings |
| title_full | Approximate Subdifferential of the Difference of Two Vector Convex Mappings |
| title_fullStr | Approximate Subdifferential of the Difference of Two Vector Convex Mappings |
| title_full_unstemmed | Approximate Subdifferential of the Difference of Two Vector Convex Mappings |
| title_short | Approximate Subdifferential of the Difference of Two Vector Convex Mappings |
| title_sort | approximate subdifferential of the difference of two vector convex mappings |
| topic | vector optimization optimality condition approximate subdifferential DC programming |
| url | https://www.mdpi.com/2227-7390/11/12/2718 |
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