Optimality conditions for solutions of constrained inverse vector variational inequalities by means of nonlinear scalarization

This work is devoted to examining inverse vector variational inequalities with constraints by means of a prominent nonlinear scalarizing functional. We show that inverse vector variational inequalities are equivalent to multiobjective optimization problems with a variable domination structure. Moreover, we introduce a nonlinear function based on a well-known nonlinear scalarization function. We show that this function is a weak separation function and a regular weak separation function under different parameter sets. Then two alternative theorems are established, which will provide the basis for characterizing efficient elements of inverse vector variational inequalities. © 2017 Journal of Nonlinear and Variational Analysis