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

Ram U. Verma

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.


Keywords


Variational inclusions; Maximal monotone mapping; Relative \mbox{$A$-maximal} monotone (RMM) mapping; Generalized resolvent operator; Generalized proximal point algorithm

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DOI: http://dx.doi.org/10.26713%2Fjims.v1i1.4

eISSN 0975-5748; pISSN 0974-875X