Filomat 2012 Volume 26, Issue 5, Pages: 1065-1073
https://doi.org/10.2298/FIL1205065M
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On V-r-invexity and vector variational-like inequalities
Mishra S.K. (Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi, India)
Laha Vivek (Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi, India)
In this paper, we consider the multiobjective optimization problems involving
the differentiable V-r-invex vector valued functions. Under the assumption of
V-r-invexity, we use the Stampacchia type vector variational-like
inequalities as tool to solve the vector optimization problems. We establish
equivalence among the vector critical points, the weak efficient solutions
and the solutions of the Stampacchia type weak vector variational-like
inequality problems using Gordan’s separation theorem under the V-r-invexity
assumptions. These conditions are more general than those appearing in the
literature.
Keywords: multiobjective optimization, V-r-invexity, vector variational-like inequality, efficiency, vector critical point