ON GENERALIZED POLYNOMIAL VARIATIONAL INEQUALITY PART 1: EXISTENCE OF SOLUTIONS

摘要

In this paper, we consider the generalized polynomial variational inequality (GPVI). By using the proposed regular condition, we establish a sufficient condition for the existence of solutions to the GPVI. The compactness and uniqueness of the solution set of the GPVI are investigated. We present an extension of Hartman-Stampacchia's theorem for the GPVI and use this result to propose sufficient conditions for the nonemptiness and compactness of the solution set of a class of the GPVI. Several illustrating examples are presented to compare obtained results with existing ones in [SIAM J. Control Optim. 33, (1995), 168-184] and others. Our main tools are the theory related to exceptional family of elements, structure of tensors, and recession cone.