A Relaxed Approximate Proximal Point Algorithm

Abstract For a maximal monotone operator T, a well-known overrelaxed point algorithm is often used to find the zeros of T. In this paper, we enhance the algorithm to find a point in $T^{-1}(0)\cap \mathcal{X}$ , where $\mathcal{X}$ is a given closed convex set. In the inexact case of our modified relaxed proximal point algorithm, we give a new criterion. The convergence analysis is quite easy to follow.