Sufficient conditions for the existence and uniqueness of minimizers for variational problems under uncertainty
Fuzzy variational problems have received significant attention over the past decade due to a number of successful applications in fields such as optimal control theory and image segmentation. Current literature on fuzzy variational problems focuses on the necessary optimality conditions for finding...
| Main Authors: | , , , , |
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| Format: | Article |
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Multidisciplinary Digital Publishing Institute
2022
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| Online Access: | http://psasir.upm.edu.my/id/eprint/103353/ |
| _version_ | 1848863997067001856 |
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| author | Verma, Mansi Chen, Chuei Yee Kilicman, Adem Ibragimov, Gafurjan Lim, Fong Peng |
| author_facet | Verma, Mansi Chen, Chuei Yee Kilicman, Adem Ibragimov, Gafurjan Lim, Fong Peng |
| author_sort | Verma, Mansi |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Fuzzy variational problems have received significant attention over the past decade due to a number of successful applications in fields such as optimal control theory and image segmentation. Current literature on fuzzy variational problems focuses on the necessary optimality conditions for finding the extrema, which have been studied under several differentiability conditions. In this study, we establish the sufficient conditions for the existence of minimizers for fuzzy variational problems under a weaker notion of convexity, namely preinvexity and Buckley–Feuring differentiability. We further discuss their application in a cost minimization problem. |
| first_indexed | 2025-11-15T13:41:48Z |
| format | Article |
| id | upm-103353 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:41:48Z |
| publishDate | 2022 |
| publisher | Multidisciplinary Digital Publishing Institute |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1033532023-06-16T07:56:15Z http://psasir.upm.edu.my/id/eprint/103353/ Sufficient conditions for the existence and uniqueness of minimizers for variational problems under uncertainty Verma, Mansi Chen, Chuei Yee Kilicman, Adem Ibragimov, Gafurjan Lim, Fong Peng Fuzzy variational problems have received significant attention over the past decade due to a number of successful applications in fields such as optimal control theory and image segmentation. Current literature on fuzzy variational problems focuses on the necessary optimality conditions for finding the extrema, which have been studied under several differentiability conditions. In this study, we establish the sufficient conditions for the existence of minimizers for fuzzy variational problems under a weaker notion of convexity, namely preinvexity and Buckley–Feuring differentiability. We further discuss their application in a cost minimization problem. Multidisciplinary Digital Publishing Institute 2022 Article PeerReviewed Verma, Mansi and Chen, Chuei Yee and Kilicman, Adem and Ibragimov, Gafurjan and Lim, Fong Peng (2022) Sufficient conditions for the existence and uniqueness of minimizers for variational problems under uncertainty. Mathematics, 10 (19). art. no. 3638. pp. 1-15. ISSN 2227-7390 https://www.mdpi.com/2227-7390/10/19/3638 10.3390/math10193638 |
| spellingShingle | Verma, Mansi Chen, Chuei Yee Kilicman, Adem Ibragimov, Gafurjan Lim, Fong Peng Sufficient conditions for the existence and uniqueness of minimizers for variational problems under uncertainty |
| title | Sufficient conditions for the existence and uniqueness of minimizers for variational problems under uncertainty |
| title_full | Sufficient conditions for the existence and uniqueness of minimizers for variational problems under uncertainty |
| title_fullStr | Sufficient conditions for the existence and uniqueness of minimizers for variational problems under uncertainty |
| title_full_unstemmed | Sufficient conditions for the existence and uniqueness of minimizers for variational problems under uncertainty |
| title_short | Sufficient conditions for the existence and uniqueness of minimizers for variational problems under uncertainty |
| title_sort | sufficient conditions for the existence and uniqueness of minimizers for variational problems under uncertainty |
| url | http://psasir.upm.edu.my/id/eprint/103353/ http://psasir.upm.edu.my/id/eprint/103353/ http://psasir.upm.edu.my/id/eprint/103353/ |