GENERAL FRAMEWORK FOR PROXIMAL POINT ALGORITHMS ON (A, η)-MAXIMAL MONOTONICIT FOR NONLINEAR VARIATIONAL INCLUSIONS

- Journal title : Communications of the Korean Mathematical Society
- Volume 26, Issue 4, 2011, pp.685-693
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2011.26.4.685

Title & Authors

GENERAL FRAMEWORK FOR PROXIMAL POINT ALGORITHMS ON (A, η)-MAXIMAL MONOTONICIT FOR NONLINEAR VARIATIONAL INCLUSIONS

Verma, Ram U.;

Verma, Ram U.;

Abstract

General framework for proximal point algorithms based on the notion of (A, )-maximal monotonicity (also referred to as (A, )-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, )-monotonicity. The obtained results generalize and unify a wide range of investigations readily available in literature.

Keywords

variational inclusions;maximal monotone mapping;(A, ) maximal monotone mapping;generalized resolvent operator;

Language

English

Cited by

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