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

Title & Authors
GENERAL FRAMEWORK FOR PROXIMAL POINT ALGORITHMS ON (A, η)-MAXIMAL MONOTONICIT FOR NONLINEAR VARIATIONAL INCLUSIONS
Verma, Ram U.;

Abstract
General framework for proximal point algorithms based on the notion of (A, $\small{{\eta}}$)-maximal monotonicity (also referred to as (A, $\small{{\eta}}$)-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, $\small{{\eta}}$)-monotonicity. The obtained results generalize and unify a wide range of investigations readily available in literature.
Keywords
variational inclusions;maximal monotone mapping;(A, $\small{\eta}$) maximal monotone mapping;generalized resolvent operator;
Language
English
Cited by
1.
General Class of Implicit Variational Inclusions and Graph Convergence on A-Maximal Relaxed Monotonicity, Journal of Optimization Theory and Applications, 2012, 155, 1, 196
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