Abstract.First a general framework for a hybrid super-relaxed proximal point algorithm based on the notion of H-maximal monotonicity is introduced, and then the convergence analysis for solving a general class of nonlinear inclusion problems is explored. The framework developed in this communication is quite suitable to generalize first-order evolution equations based on the generalized nonlinear Yosida regularization/ approximation and beyond. Further more, the obtained results can also be applied to generalize Douglas-Rachford splitting methods for finding the zero of the sum of two generalized maximal monotone mappings.

Received: April 1, 2010

AMS Subject Classification: 49J40, 65B05

Key Words and Phrases: variational inclusions, maximal monotone mapping, H-maximal monotone mapping, generalized resolvent operator

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 60
Issue: 4