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Mathematics
Volume 10
Issue 19
10.3390/math10193638
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Article

Sufficient Conditions for the Existence and Uniqueness of Minimizers for Variational Problems under Uncertainty

by
Mansi Verma
1,†,
Chuei Yee Chen
1,*,†,
Adem Kılıçman
2,
Gafurjan Ibragimov
1 and
Fong Peng Lim
1
1
Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia
2
Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2022, 10(19), 3638; https://doi.org/10.3390/math10193638
Submission received: 25 August 2022 / Revised: 14 September 2022 / Accepted: 20 September 2022 / Published: 5 October 2022
(This article belongs to the Special Issue Uncertainty Analysis, Decision Making and Optimization)
Versions Notes

Abstract

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.
Keywords: fuzzy variational problem; existence of minimizer; sufficient conditions; invex sets; preinvex functions fuzzy variational problem; existence of minimizer; sufficient conditions; invex sets; preinvex functions

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MDPI and ACS Style

Verma, M.; Chen, C.Y.; Kılıçman, A.; Ibragimov, G.; Lim, F.P. Sufficient Conditions for the Existence and Uniqueness of Minimizers for Variational Problems under Uncertainty. Mathematics 2022, 10, 3638. https://doi.org/10.3390/math10193638

AMA Style

Verma M, Chen CY, Kılıçman A, Ibragimov G, Lim FP. Sufficient Conditions for the Existence and Uniqueness of Minimizers for Variational Problems under Uncertainty. Mathematics. 2022; 10(19):3638. https://doi.org/10.3390/math10193638

Chicago/Turabian Style

Verma, Mansi, Chuei Yee Chen, Adem Kılıçman, Gafurjan Ibragimov, and Fong Peng Lim. 2022. "Sufficient Conditions for the Existence and Uniqueness of Minimizers for Variational Problems under Uncertainty" Mathematics 10, no. 19: 3638. https://doi.org/10.3390/math10193638

APA Style

Verma, M., Chen, C. Y., Kılıçman, A., Ibragimov, G., & Lim, F. P. (2022). Sufficient Conditions for the Existence and Uniqueness of Minimizers for Variational Problems under Uncertainty. Mathematics, 10(19), 3638. https://doi.org/10.3390/math10193638

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