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General Variational Inequalities: Existence of Solutions, Tikhonov-Type Regularization, and Well-posedness
Tran Van Nghi
,
Nguyen Nang Tam
Abstract
In this paper, we present necessary and sufficient conditions for existence and uniqueness of solutions of general variational inequalities (GVIs). A Tikhonov-type regularization method to find a solution of GVIs is proposed. Finally, under suitable conditions, we prove that the well-posedness of a GVI is equivalent to the solution existence and uniqueness. The obtained results are compared with the previous ones. In particular, our results generalize corresponding ones for inverse variational inequalities.