Abstract
The theory of vector variational inequalities began with the pioneer work of F. Giannessi in 1980 where he extended the classical variational inequality for vector-valued functions in the setting of finite dimensional spaces. He also provided some applications to alternative theorems, quadratic programs and complementarity problems. Since then, a large number of papers have appeared in the literature on different aspects of vector variational inequalities. These references are gathered in the bibliography. Later, it is proved that the theory of vector variational inequalities is a powerful tool to study vector optimization problems. In this chapter, we give an introduction to vector variational inequalities, existence theory of their solutions and some applications to vector optimization problems.
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