AN APPROXIMATE NONLINEAR PROXIMAL PREDICTION-CORRECTION ALGORITHM FOR MAXIMAL MONOTONE OPERATORS

Abstract

This paper introduces an approximate nonlinear proximal prediction-correction algorithm for finding the zero points of  T(.), where T is a maximal monotone operator. In the prediction step, the presented algorithm allows for constant relative error tolerance which should be easier to verify and enforce in practice than those given in earlier analysis of approximate generalized proximal point algorithms. In the correction step, to make more progress, a general decent direction and a suitable step length are used. And the global convergence is easily established under weaker conditions on the algorithm parameters. As for applications, we give two methods, one is for solving monotone variational inequalities and the other is for the hoice of the decent direction in the correction step.