General Proximal Point Algorithmic Models and Nonlinear Variational Inclusions Involving RMM Mappings

Abstract

The proximal point algorithms based on relative $A$-maximal monotonicity (RMM) is introduced, and then it is applied to the approximation solvability of a general class of nonlinear inclusion problems using the generalized resolvent operator technique.  This algorithm seems to be more
application-oriented to solving nonlinear inclusion problems. 
Furthermore, the obtained result could be applied to generalize the Douglas-Rachford splitting method to the case of RMM mapping based on the generalized proximal point algorithm.