Algorithms For Variational Inequality In Finite Dimensional Norm Space

This paper mainly considers the algorithms for variational inequalityin finite dimensional norm space. There are a lot of algorithms for variationalinequality in Euclidean space, but the algorithms for variational inequality infinite dimensional norm space need a rather strong monotonicity condition. Inthe first chapter, we present a method for solving variational inequality in finitedimensional norm space, under a relatively weak monotonicity condition. Weprove that the sequence generated by our method converges to a solution of vari-ational inequality, and analyze the complexity. In the second chapter, we presenta method for general variational inequality in finite dimensional norm space.