Geodesic
Relations between multidimensional interval-valued variational problems and variational inequalities
Kybernetika, Tome 58 (2022) no. 4, pp. 564-577
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In this paper, we introduce a new class of variational inequality with its weak and split forms to obtain an $LU$-optimal solution to the multi-dimensional interval-valued variational problem, which is a wider class of interval-valued programming problem in operations research. Using the concept of (strict) $LU$-convexity over the involved interval-valued functionals, we establish equivalence relationships between the solutions of variational inequalities and the (strong) $LU$-optimal solutions of the multi-dimensional interval-valued variational problem. In addition, some applications are constructed to illustrate the established results.
In this paper, we introduce a new class of variational inequality with its weak and split forms to obtain an $LU$-optimal solution to the multi-dimensional interval-valued variational problem, which is a wider class of interval-valued programming problem in operations research. Using the concept of (strict) $LU$-convexity over the involved interval-valued functionals, we establish equivalence relationships between the solutions of variational inequalities and the (strong) $LU$-optimal solutions of the multi-dimensional interval-valued variational problem. In addition, some applications are constructed to illustrate the established results.
DOI : 10.14736/kyb-2022-4-0564
Classification : 26B25, 26D10, 49J40, 90C30
Keywords: $LU$-convexity; $LU$-optimal solution; multi-dimensional inter-valued variational problem; variational inequality 
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Jayswal, Anurag; Baranwal, Ayushi. Relations between multidimensional interval-valued variational problems and variational inequalities. Kybernetika, Tome 58 (2022) no. 4, pp. 564-577. doi: 10.14736/kyb-2022-4-0564

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