Abstract
When the objective function involved in the vector optimization problem is not necessarily differentiable, then the method to solve VOP via corresponding vector variational inequality problems is no longer valid. We need to generalize the vector variational inequality problems for set-valued maps. There are several ways to generalize vector variational inequality problems discussed in chapter “Vector Variational Inequalities”. The main objective of this chapter is to generalize the vector variational inequality problems for set-valued maps and to present the existence results for such generalized vector variational inequality problems with or without monotonicity assumption. We also present some relations between a generalized vector variational inequality problem and a vector optimization problem with a nondifferentiable objective function. Several results of this chapter also hold in the setting of Hausdorff topological vector spaces, but for the sake of convenience, our setting is Banach spaces.
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Ansari, Q.H., Köbis, E., Yao, JC. (2018). Generalized Vector Variational Inequalities. In: Vector Variational Inequalities and Vector Optimization. Vector Optimization. Springer, Cham. https://doi.org/10.1007/978-3-319-63049-6_8
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DOI: https://doi.org/10.1007/978-3-319-63049-6_8
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