Relations between multidimensional interval-valued variational problems and variational inequalities

Anurag Jayswal; Ayushi Baranwal

Kybernetika (2022)

  • Volume: 58, Issue: 4, page 564-577
  • ISSN: 0023-5954

Abstract

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In this paper, we introduce a new class of variational inequality with its weak and split forms to obtain an L U -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) L U -convexity over the involved interval-valued functionals, we establish equivalence relationships between the solutions of variational inequalities and the (strong) L U -optimal solutions of the multi-dimensional interval-valued variational problem. In addition, some applications are constructed to illustrate the established results.

How to cite

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Jayswal, Anurag, and Baranwal, Ayushi. "Relations between multidimensional interval-valued variational problems and variational inequalities." Kybernetika 58.4 (2022): 564-577. <http://eudml.org/doc/299585>.

@article{Jayswal2022,
abstract = {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.},
author = {Jayswal, Anurag, Baranwal, Ayushi},
journal = {Kybernetika},
keywords = {$LU$-convexity; $LU$-optimal solution; multi-dimensional inter-valued variational problem; variational inequality},
language = {eng},
number = {4},
pages = {564-577},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Relations between multidimensional interval-valued variational problems and variational inequalities},
url = {http://eudml.org/doc/299585},
volume = {58},
year = {2022},
}

TY - JOUR
AU - Jayswal, Anurag
AU - Baranwal, Ayushi
TI - Relations between multidimensional interval-valued variational problems and variational inequalities
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 4
SP - 564
EP - 577
AB - 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.
LA - eng
KW - $LU$-convexity; $LU$-optimal solution; multi-dimensional inter-valued variational problem; variational inequality
UR - http://eudml.org/doc/299585
ER -

References

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