Existence and Stability for Generalized Polynomial Vector Variational Inequalities

We investigate the generalized polynomial vector variational inequality (GPVVI), which is a natural generalization of generalized polynomial variational inequality (GPVI) and vector variational inequality (VVI). Due to the scalarization method, which is a powerful technique in vector optimization, we establish a relationship between the Pareto solution sets of the GPVVI and the solution set of the GPVI. By using the concept on exceptional family of elements, recession cone, and positive semi-definiteness of matrices, we present sufficient conditions for the nonemptiness and boundedness of the Pareto solution sets of the GVVI. We present sufficient conditions for the upper/lower semicontinuity of the weak Pareto solution map and the stability for GVVIs. Finally, we obtain some applications to polynomial variational inequality. The presented result develops and complements the previous ones.