Nonsmooth weighted variational inequalities and nonsmooth vector optimization

In this paper, we use weighted sum method to study nonsmooth vector variational inequalities and nonsmooth vector optimization problem. In particular, we introduce nonsmooth weighted variational inequalities (in short. NWVI) and study some relationships among XWVT, nonsmooth vector variational inequalities (in short, NWI), nonsmooth weighted optimization problem (in short, NWOP) and nonsmooth vector optimization problem (in short. NVOP). We establish some existence results for solutions of (NWI) and (NWVI) under weighted pseudomonotonicity or densely weighted pseudomonotonicity. As applications of our results, some existence results for solutions of NWOP and NVOP for nondifferentiable functions by using the equivalence relations among NWI, NWVI, XWOP and VOP can be easily derived.