The Proximal Point Algorithm for Variational inequalities

We study the convergence analysis of the sequence generated by the proximal point algorithm for variational inequalities of pseudo-monotone type in Euclidean spaces. We also introduce the concept of cyclic pseudo-monotonicity in order to prove the convergence of the sequence generated by the proximal point algorithm with weaker condition on the regularization parameter. Finally, in order to numerical purposes, we study the inexact version of the proximal point algorithm for the pseudo-monotone operator and we prove the convergence of the sequence to a solution of the variational inequality.

Keywords:

Convergence analysis , inexact version of the proximal point algorithm , proximal point algorithm , pseudo-monotone operator.