Weak and strong convergence for some generalized proximal point algorithms are proved. These algorithms include the Eckstein and Bertsekas generalized proximal point algorithm, a contraction-proximal point algorithm, and inexact proximal point algorithms. Convergence rate is also considered.

In this article, we propose a modified Korpelevich's method for solving variational inequalities. Under some mild assumptions, we show that the suggested method converges strongly to the minimum-norm solution of some variational inequality in an infinite-dimensional Hilbert space.