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

Mansi Verma, Chuei Yee Chen (), Adem Kılıçman, Gafurjan Ibragimov and Fong Peng Lim
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Mansi Verma: Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia
Chuei Yee Chen: Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia
Adem Kılıçman: Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia
Gafurjan Ibragimov: Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia
Fong Peng Lim: Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, Serdang 43400 UPM, Selangor, Malaysia

Mathematics, 2022, vol. 10, issue 19, 1-15

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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