The Generalized Vector Variational Inequalities and the Generalized Dual Models
广义向量变分不等式和广义对偶模型

In this paper, the nonsmooth vector optimization problem with inequality constraints in real Banach space is studied. First, in terms of the lower directional derivatives, the generalized Minty type vector variational inequalities are introduced. Then, the optimality condition of the problem (VP) is obtained.Finally, the generalized dual model of the problem (VP) is presented with the help of upper subdifferential of function, and a weak duality theorem is given.