Modified Proximal Algorithms for Finding Solutions of the Split Variational Inclusions

Split Monotone Variational Inclusions

Based on the very recent work by Censor-Gibali-Reich [7], we propose an extension of their new variational problem (Split Variational Inequality Problem) to monotone variational inclusions. Relying on the Krasnoselskii-Mann Theorem for averaged operators, we analyze an algorithm for solving a new split monotone inclusions under weaker conditions. Our results improve and develop previously discu...

Projection Algorithms for Variational Inclusions

General Framework for Proximal Point Algorithms on (a, Η)-maximal Monotonicity for Nonlinear Variational Inclusions

General framework for proximal point algorithms based on the notion of (A, η)-maximal monotonicity (also referred to as (A, η)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 correspo...

Modified Proximal point algorithms for finding a zero point of maximal monotone operators, generalized mixed equilibrium problems and variational inequalities

* Correspondence: poom. [email protected] Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangmod, Thrungkru, Bangkok 10140, Thailand Full list of author information is available at the end of the article Abstract In this article, we prove strong and weak convergence theorems of modified proximal point algorithms for finding a common elemen...

Super-Relaxed (η)-Proximal Point Algorithms, Relaxed (η)-Proximal Point Algorithms, Linear Convergence Analysis, and Nonlinear Variational Inclusions

We glance at recent advances to the general theory of maximal set-valued monotone mappings and their role demonstrated to examine the convex programming and closely related field of nonlinear variational inequalities. We focus mostly on applications of the super-relaxed η proximal point algorithm to the context of solving a class of nonlinear variational inclusion problems, based on the notion ...