ON VECTOR VARIATIONAL INEQUALITIES AND NONSMOOTH VECTOR OPTIMIZATION PROBLEMS WITH GENERALIZED APPROXIMATE INVEXITY

In this paper, we consider two types of vector variational inequal-ities namely, Minty vector variational inequalities(MVVI) and Stampacchia Vector variational inequalities(SVVI) for a nonsmooth vector optimization problem involving locally Lipschitz generalized approximate invex functions. We formulate approximate (MVVI) and (SVVI) involving Clarke's generalized Jacobians and exploit them to characterize an approximate efficient solutions of the nonsmooth vector optimization problems to approximate (MVVI) and (SVVI) of different types. We also give an example to show the validity of main results. Our newly proved results generalize some well-known results in the literature.