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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.13 no.3 Temuco oct. 2011

http://dx.doi.org/10.4067/S0719-06462011000300010 

CUBO A Mathematical Journal Vol.13, Nº03, (185-196). October 2011

 

Linear Convergence Analysis for General Proximal Point Algorithms Involving (H,η)- Monotonicity Frameworks

 

Ram U. Verma

Texas A&M University at Kingsville, Department of Mathematics, Kingsville, Texas 78363, USA. email: verma99@msn.com


ABSTRACT

General framework for the generalized proximal point algorithm, based on the notion of (H,r)- 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.

Keywords. General cocoerciveness, Variational inclusions, Maximal monotone mapping, (H,r) - monotone mapping, Generalized proximal point algorithm, Generalized resolvent operator.

Mathematics Subject Classification: 49J40, 47H10, 65B05.


RESUMEN

Se desarrolla un marco general para el algoritmo de punto proximal generalizado, basado en la noción de (H,r)- monotonia. Se examina el analisis de convergencia lineal para el algoritmo de punto proximal generalizado en el contexto de la resolucion de una clase de inclusiones no lineales variacional. Los resultados obtenidos generalizan y unifican una amplia gama de problemas en el contexto de lograr la convergencia lineal de los algoritmos punto proximal.


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Received: September 2010. Revised: November 2010.