Multiobjective variational problems and generalized vector variational-type inequalities
Jayswal, Anurag1 ; Singh, Shipra1
1 Department of Applied Mathematics, Indian School of Mines, Dhanbad-826 004, Jharkhand, India.
RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 1, pp. 211-225.

The purpose of this paper is to generalize the vector variational-type inequalities, formulated by Kim [J. Appl. Math. Comput. 16 (2004) 279–287], by setting the norms into Minty and Stampacchia forms. We also demonstrate the relationships between these generalized inequalities and multiobjective variational problems, by using the notions of strongly convex functionals. The theoretical developments are illustrated through numerical examples.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2016017
Classification : 90C30, 90C29, 49J40
Mots-clés : Multiobjective variational problem, generalized Minty vector variational-type inequality, generalized Stampacchia vector variational-type inequality, strongly convex functional, strongly preconvex functional
Jayswal, Anurag 1 ; Singh, Shipra 1

1 Department of Applied Mathematics, Indian School of Mines, Dhanbad-826 004, Jharkhand, India. 
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Jayswal, Anurag; Singh, Shipra. Multiobjective variational problems and generalized vector variational-type inequalities. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 1, pp. 211-225. doi : 10.1051/ro/2016017. http://www.numdam.org/articles/10.1051/ro/2016017/

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