The over-relaxed proximal point algorithm based on H-maximal monotonicity design and applications

First the general framework for a generalized over-relaxed proximal point algorithm using the notion of H-maximal monotonicity (also referred to as H-monotonicity) is developed, and then the convergence analysis for this algorithm in the context of solving a general class of nonlinear inclusion problems is examined along with some auxiliary results on the resolvent operators corresponding to H-maximal monotonicity.