General Proximal Point Algorithmic Models and Nonlinear Variational Inclusions Involving RMM Mappings
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.
eISSN 0975-5748; pISSN 0974-875X