General framework for proximal point algorithms on $(A,\eta)$-maximal monotonicity for nonlinear variational inclusions
Commun. Korean Math. Soc. 2011 Vol. 26, No. 4, 685-693
https://doi.org/10.4134/CKMS.2011.26.4.685
Published online December 1, 2011
Ram U. Verma
Seminole State College oF Florida
Abstract : General framework for proximal point algorithms based on the notion of $(A,\eta)$-maximal monotonicity (also referred to as $(A,\eta)$-monotonicity in literature) is developed. Linear convergence analysis for this class of algorithms to the context of solving a general class of nonlinear variational inclusion problems is successfully achieved along with some results on the generalized resolvent corresponding to $(A,\eta)$-monotonicity. The obtained results generalize and unify a wide range of investigations readily available in literature.
Keywords : variational inclusions, maximal monotone mapping, $(A,\eta)$-maximal monotone mapping, generalized resolvent operator
MSC numbers : 49J40, 65B05
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