On relationships between vector optimization problems and vector variational inequalities using directional convexificators

In this work, we formulate the vector variational inequalities of Stampacchia and Minty types in terms of directional convexificators, and relate them to a vector optimization problem. Our approach consists of using a suitable directional generalized convexity, given in terms of directional convexificators, to help us figure out the necessary and sufficient conditions for a point to be an efficient solution to the vector optimization problem. We also investigate the weak versions of the vector variational inequalities and provide several results for determining weak efficient solutions. An example illustrating both our findings and the limits of some earlier research is provided.