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

Authors

  • Ram U. Verma Florida Institute of Technology, Department of Mathematical Sciences, Melbourne, Florida 32901, USA

DOI:

https://doi.org/10.26713/jims.v1i1.4

Keywords:

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

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.

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CITATION

How to Cite

Verma, R. U. (2009). General Proximal Point Algorithmic Models and Nonlinear Variational Inclusions Involving RMM Mappings. Journal of Informatics and Mathematical Sciences, 1(1), 15–25. https://doi.org/10.26713/jims.v1i1.4

Issue

Vol. 1 No. 1 (2009)

Section

Research Articles

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