Generalized Eckstein–Bertsekas proximal point algorithm based on AA-maximal monotonicity design

A general design for the Eckstein–Bertsekas proximal point algorithm, using the notion of the AA-maximal monotonicity, is developed. Convergence analysis for the generalized Eckstein–Bertsekas proximal point algorithm in the context of solving a class of nonlinear inclusion problems is explored. Some auxiliary results of interest involving AA-maximal monotone mappings are also included. The obtained results generalize investigations on general maximal monotonicity and beyond.