Linear convergence analysis for general proximal point algorithms involving (H, Î·) âˆ’ monotonicity frameworks

Ram U. Verma

doi:10.4067/S0719-06462011000300010

Linear convergence analysis for general proximal point algorithms involving (H, Î·) âˆ’ monotonicity frameworks

Authors

Ram U. Verma Texas A&M University at Kingsville, Department of Mathematics, Kingsville, Texas 78363, USA.

DOI:

https://doi.org/10.4067/S0719-06462011000300010

Keywords:

General cocoerciveness, Variational inclusions, Maximal monotone mapping, (H, Î·) âˆ’ monotone mapping, Generalized proximal point algorithm, Generalized resolvent operator

Abstract

General framework for the generalized proximal point algorithm, based on the notion of (H, Î·) âˆ’ monotonicity, is developed. The linear convergence analysis for the generalized proximal point algorithm to the context of solving a class of nonlinear variational inclusions is examined, The obtained results generalize and unify a wide range of problems to the context of achieving the linear convergence for proximal point algorithms.

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Published

2011-10-01

How to Cite

[1]

R. U. Verma, “Linear convergence analysis for general proximal point algorithms involving (H, Î·) âˆ’ monotonicity frameworks”, CUBO, vol. 13, no. 3, pp. 185–196, Oct. 2011.